It is the holy grail of policy-makers everywhere, and never more so than in these chastened economic times: how to get more bang for your buck. And nowhere is the attempt to link what goes in with what comes out more enthusiastically promoted than in education.

Educationalists have spent entire careers trying to work out the link between spending on schools and pupil performance, and how that might be measured. So far, however, their efforts have proved unable to provide a consensus on that most pressing of questions: how to get top grades on a budget.

But if anyone has the answer, there is a fair chance they are working in what must count as one of the wettest places in England, perched above the market town of Bakewell on the top of the Derbyshire Dales. On this spot sits a school that has been crowned as the most efficient comprehensive in the country.

Lady Manners School has been in existence since 20 May, 1636 when Grace, the lady in question, set up a fund to pay for the education of “the poor boys of Bakewell”. Exactly 300 years later, her descendant, by then the 9th Duke of Rutland, laid the foundation stone for a new building on its present site that still forms the hub of the school.

The original fund produced the sum of pound;15 a year to pay for the school’s lone teacher. Today, its annual budget is a shade over pound;6 million, but if that seems a steep increase, even given 375 years of inflation, the school gets good value for money.

Proof of this comes courtesy of Michael Gove. When the education secretary released figures on school spending earlier this year - the first time they had been published on an individual school level - his avowed aim was to create the education equivalent of a consumer price-comparison website. Parents would be able to look at how much schools spend and what results they get, he said, and work out which headteachers were getting the most for their money.

Subsequently, The Sunday Times commissioned data analysts to produce a table correlating spending figures with exam results. The analysts took the spend per pupil figures helpfully provided by Mr Gove and last year’s A-level results to work out the cost of getting 100 level-three points at A-level, the equivalent of almost half an A grade.

Their findings showed a wide variation, from schools that spent pound;334 to get 100 points to pound;2,733 at the other end of the scale. Predictably enough, selective schools, with their ability to take the brightest children and the most likely to get good grades - and perhaps with less need of effort on the part of schools to get those grades - came top of the list.

But on a more levelled playing field, it was Lady Manners that came top of the comprehensives, spending about pound;428 per 100 A-level points. Headteacher Duncan Meikle is predictably pleased, although his delight is perhaps tinged with a touch of embarrassment.

“When you consider how many schools there are in the country, to come out as number one is obviously a great achievement,” he says. “But, as with any league table, you have to take it with a pinch of salt. There will be other factors involved.”

Mr Meikle is aware that one of the reasons Lady Manners does so well in the analysis is beyond his control. If his actions can affect the grades pupils get, he is largely powerless to influence the other side of the equation: the funding.

At pound;4,000 per pupil, Lady Manners spends much less than many other schools, where expenditure can reach pound;14,000 per child. An active parent- teacher association means that, of this sum, about pound;370 per pupil is self- generated. But the bulk of its income, as with most schools, comes from the local authority, in its case, Derbyshire County Council.

And it is in this allocation that the bulk of the difference lies. Derbyshire is a largely rural and relatively affluent area, so the council gets less money to spend on education than urban authorities suffering greater social and economic problems.

At Lady Manners, for example, although Mr Meikle says the school’s catchment area has pockets of deprivation, 4 per cent of pupils qualify for free school meals, against a national average of 14 per cent. The school’s relatively low allocation partly reflects this.

“The effect is that this school doesn’t end up with as much money as it would have if you picked it up and planted it somewhere else,” says Mr Meikle.

There are other factors underpinning Lady Manners’ table position. It is a large school, with 1,500 pupils, of whom 350 are in the sixth-form. This means it can both offer a wider range of subjects - 30 - at post-16 level than many other schools, and it benefits from economies of scale: classes of 20 students are not unusual among popular subjects, a rarity at A- level.

Given these factors, it came as little surprise to Mr Meikle when Lady Manners came top of the table. “We’re always likely to be pretty high in that sort of table,” he says. “If the exercise was done retrospectively, chances are we would be high up every year, although not necessarily first.”

But that does not mean comparing value for money between schools is simply a matter of comparing budgets. Schools still have to get good results. Lady Manners scored an impressive 938 points per student in last year’s A- levels, compared with the average for England of 727 and the Derbyshire average of 755.

There is no alchemy involved, no mysterious formula for success. Mr Meikle does not claim that Lady Manners is doing anything that other schools do not also do. But they are doing it well.

Attendance is one focus. There is no let-up in making sure students are in lessons just because they are in the sixth-form. It helps that Bakewell is a 15-minute walk down a hill, so students are less likely to go off-site at lunchtime and not return, but still, at 94.5 per cent, sixth-form attendance is high. Year 12 has the second highest attendance rate in the school, after Year 7.

Sixth-former Naomi Mawhood, 18, has been at the sharp end of this. After she missed three biology lessons in a row, her form tutor was asked to chase her up. “You get picked up very, very quickly if you are absent,” Naomi says.

Tim Sizer, head of sixth-form, says staff make extensive use of tracking data to set targets and monitor students’ progress. Some subjects, such as maths, assign students a mentor - staff who do not teach them but are available to help on an informal basis when necessary.

In truth, many of these strategies will be in place up and down the country. What makes Lady Manners stand out in the value for money table is that its approach produces results in combination with its low level of funding.

But such comparisons need to be approached with a great deal of caution, according to Anna Vignoles, professor of the economics of education at London University’s Institute of Education and a researcher into school efficiency. While she is all in favour of transparency, she says tables that compare value for money between schools should carry a health warning.

“There is a danger that if you just look at the statistical correlation you will get completely the wrong answer,” she says. She says efforts to find a link between spending and pupil achievement have so far proved largely fruitless, the one exception being studies that found the additional money spent on primary schools between 1997 and 2006 had a positive impact.

She says there are a number of factors which determine whether the same grades cost more to produce in one school than another, and the most important of these is prior attainment. Here Lady Manners has another advantage: pupils arrive at the school already with above-average levels of achievement.

Looking at the difference a school has made to pupils’ achievement - through the contextual value-added measure - could provide a “meaningful insight” into the relationship between spending and attainment, Professor Vignoles says, although even here the interpretation would come with caveats about its use.

But this does not mean that the straight-forward value-for-money comparisons are worthless. Provided that appropriate noises are made about context, Professor Vignoles says they can give some interesting results.

“If you are comparing schools in similar positions, you will get some useful answers,” she says. Tracking data over time would be even more rewarding, she says, as it would iron out variations caused in years where results were exceptionally good, or unusually bad, for example.

Malcolm Trobe, policy director at the Association of School and College Leaders (ASCL), believes broad comparisons can be made, but argues that the range of influences on school spending mean the data must be handled with care. Meaningful judgments can only be made in conjunction with other information, he adds.

Schools with a large number of pupils with special needs, for example, will often allocate a substantial proportion of their budget to support staff. “You have to dig into the detail to understand exactly what is in there,” he says. “But if a school is well funded in a leafy suburb and is not doing very well, you may be able to ask questions in relation to its achievement.”

Alan Smithers, professor of education at Buckingham University, too, believes it is possible to use the data to make meaningful judgments.

While he warns against straightforward comparisons, he says analysis can give an indication of how schools are performing, when set against schools in similar circumstances, serving similar catchment areas and with similar levels of funding.

“You could ask why one school is getting a lot of money and rather poor results but another school is getting the same amount of money and is doing rather well,” he says.

But he points out that both a school’s budget and its results are affected by factors outside its control. Schools get extra money if they have a higher proportion of pupils on free school meals or with special needs, but also have to provide extra support. Small schools will often show up as more expensive, he says, as will rural schools that rely on extra support to keep them open when numbers are low and new schools that have high start-up costs.

Well-established schools can also have an inbuilt advantage, he says, in that if they are oversubscribed they can operate a process of covert selection, skewing their intake towards those who are already above- average achievers.

But Professor Smithers believes the data is still useful, even though it may not lend itself to the purposes that the education secretary intends. “It shows the huge variation in funding per pupil, but it should not be used as the basis for policy-making,” he warns. “Mr Gove is going too far when he says parents should be poring over the figures and making decisions on that basis.”

Understandably, schools at the other end of the table to Lady Manners are sceptical of the value of these comparisons. Propping up the rest is the Skinners’ Company’s School for Girls in Hackney, east London, which closed last summer, to be replaced by Skinners’ Academy. But next to bottom was Deansfield Community School in Wolverhampton.

The school spends just over pound;8,000 per pupil, compared with the pound;4,000 at Lady Manners, and spent pound;2,387 for every 100 A-level points, more than five times the amount spent at Lady Manners.

But headteacher Dean Coombes points out that Deansfield is at a disadvantage that does not appear in the tables: its sixth form opened just eight years ago, and, while Lady Manners has 350 post-16 students, Deansfield has 33.

While these numbers inevitably affect the school’s “efficiency”, he says the sixth form brings a dimension that is hard to reflect in tables. The introduction of post-16 education to Deansfield is a key part of raising aspirations among the local community, which has helped improve GCSE results from 19 per cent achieving five A*-Cs not including English and maths to an anticipated 60 per cent A*-Cs with English and maths this summer.

“These students are trail-blazers,” says Mr Coombes. “In a community where over 50 per cent of adults have no qualifications at all they are changing their community.”

He says some of the school’s sixth-formers also need to work part-time, reducing the number of qualifications they take and so the number of points they can gain. “We are sometimes part of the compromise that comes from pursuing education alongside paying bills,” he adds.

He is reluctant to see education reduced to “a price-comparison site based on points scores and funding”, but is also realistic enough to recognise that, particularly in the present financial situation, schools can expect more of these sorts of judgments.

Mr Coombes believes the spending data could have some value, as a prompt to a discussion about whether education can be assessed by measures such as value-for-money. But for his part, he is in no doubt where he stands. “If parents and families are going to be encouraged to make decisions about the quality of education based solely on mute data, will we lose something valuable?” he asks.

But if this is Mr Gove’s aim, there is a fair amount of scepticism that it will come to pass. Malcolm Trobe at the ASCL says that while the information is useful to schools, he finds it hard to see that many parents will avail themselves of the data.

He also points out that as it does not include academies, which have different funding arrangements, it is not complete. As the number of academies increases, this omission will increase in importance.

“It will be interesting for schools to compare their expenditure, but I don’t think it is particularly helpful for parents,” he says. “Most parents are focused on the outcomes and what else a school provides, such as extra-curricular activities or whether it has a good record on behaviour.

“Those are the sorts of questions parents are interested in, not how much money the school is spending.”

Even at Lady Manners, Mr Meikle is not convinced that parents will take much notice of the school’s lofty position in the table. While a few parents commented on it at a Year 9 parents’ evening a few days after it was published, the headteacher does not expect the effect to last.

“I don’t think parents make a decision on the basis of league tables,” he says. “Meeting the staff, looking around the school and feeling comfortable here are much more important.”

Few people would argue against having more information on how public money is spent, particularly when it is in increasingly short supply. But if Mr Gove’s intention was to turn parents into value-conscious consumers, eager to get as good a deal from education as they do from insurance, it seems he has some way to go yet.