The numbers could hardly offer more of a contradiction. Judged by completion rates of less than one in three, apprenticeships - modern apprenticeships as were - would surely be judged a failure.

Yet with satisfaction rates over 90 per cent for employers and trainees alike, and more than a quarter of 16-year-olds now choosing them, they count as a rare example of a popular qualification that seems to deliver.

Perhaps it’s precisely because of that glaring disjunction that mutterings continue to be heard even as employers, providers and politicians pledge their support to apprenticeships’ expansion and proclaim their success.

Earlier this month, training providers warned they would be forced to turn away trainees if more funding were not forthcoming. Meanwhile, colleges fear the very youngsters most in need of apprenticeships as a route into employment are being left behind.

Both fears are a result of apprenticeships’ growing success. The funding squeeze is thanks to improving completion rates which mean trainees are staying on longer. At the same time, a nationwide advertising blitz has seen applications rise - allowing employers to be more choosy.

A bullish Stephen Gardner, director of work-based learning at the Learning and Skills Council, declares himself “very pleased”. “The numbers of young people coming forward are tremendous, and a lot more employers are taking an interest,” he says.

The LSC says it is on course to meet its target of signing up 175,000 new apprentices this academic year.

An interim report by the government-appointed apprenticeships task force - largely made up of employers - found apprentices had higher productivity, better career prospects and greater job satisfaction than their peers.

But the picture can be patchy. Recruitment is strong in traditional areas such as construction and engineering, but disappointing in sectors such as the public services. Completion rates are a serious concern.

Or are they? Graham Hoyle, chief executive of the Association of Learning Providers, says: “You’re looking at people who have jobs, and change those jobs, which is quite different from students who simply don’t finish their course.”

Many apparent failures can mask success stories. These include trainees leaving apprenticeships because they find better-paid jobs, or even promotions. “It’s difficult to describe that as failure,” Mr Hoyle says.

“It seems to me an effective working of the employment market.”

It is particularly marked in sectors such as retail and hospitality which have high staff turnover and no tradition of apprenticeships. And, like all workers, trainees are vulnerable to redundancy when business is bad.

But some employers are perhaps too pragmatic. Once they feel their staff have gained the skills they need, they pull out.

The LSC and the ALP agree “cultural change” is needed among employers and trainees. The LSC hopes its advertising will convince more people of the value of completing courses. A better solution, some say, would be to make apprenticeships more portable from job to job.

Providers would like to see each sector develop a common core which apprentices could continue to follow in a new job. Sir John Cassels, of the apprenticeships task force, suggests trainees should earn credits as they gain skills during their apprenticeship.

The LSC, which registers all new apprentices, says it is working with sector skills councils to help them to keep track of their trainees.

“Providers must work with each other, so if a young person goes to another part of the country, they can pass their records across,” Mr Gardner says.

“And we need employers to ask new recruits what training they’ve been doing.”

Another trend affecting completion rates is the development of selection processes by employers as more young people apply for apprenticeships.

That, according to Mr Hoyle, is likely to mean basic skills tests for applicants. Providers still question whether they should be taking on apprentices who have problems with literacy and numeracy, arguing they have a right to expect that their employees arrive with functional communication and number skills.

This is a contentious area. Mr Gardner says angrily that he has “no time” for those who believe it is not the job of training providers to set right what schools have failed to do.

Talk of employers being selective about recruitment alarms FE colleges, which form a relatively small proportion of apprenticeship training providers but fear being left to pick up the pieces.

“Selection leaves a rump of young people who aren’t provided for,” warns Maggie Scott, the Association of Colleges’ acting director of learning and qualifications. “How do you engage and motivate these young people? They’ve failed the academic route, failed their GCSEs and now they’re being turned away by employers.”

One solution could lie in the new “hybrid” apprenticeships. Students begin their training at college, spending perhaps a year developing basic skills and work skills, before joining an employer to complete their apprenticeship. Finding enough employers, however, is a problem.

The college-based Entry to Employment programme is another option, taken by 60,000 young people last year. That in turn has boosted completion rates.

Mr Gardner said: “In the past we were setting young people up to fail.”

But colleges fear that, in the wake of the Government’s response to the Tomlinson Report, funding for these alternatives is uncertain.

“Tomlinson was supposed to make education accessible for all,” Ms Scott says. “The white paper has really turned its back on the needs of some of those groups of young people, and made it harder for them to find a way through.”

As elsewhere, there is disappointment at the Government’s response to Tomlinson, although Sir John says: “I don’t think it means ministers are any less interested in making a success of apprenticeships.”

Certainly they continue to set challenging targets: 300,000 completed apprenticeships by 2008, a figure that requires annual completions to rise from below 50,000 to almost 80,000.

Ms Scott fears it will be tough to find enough employers, while the stark measure of success and failure may drive providers to the wall and put off colleges from getting involved.

But in the end, it may come down to cash. Mr Gardner admits there is pressure on LSC budgets. Unusually, providers commiserate with his predicament. “I have real sympathy for the Government,” says Mr Hoyle. “It has set out objectives that are being realised. The problem is, that success costs money.”