Loic Menzies, a former teacher and now director of the education and youth ‘think and action-tank’ LKMco, writes:

There are 102 mainstream schools in England that exhibit the strange phenomenon of a “reverse gap”, where disadvantaged pupils outperform their peers. While schools battling to shave every possible percentage point from their attainment gap could be forgiven a moment’s jealousy, a more detailed look tells us more about our polarised education system than anything else.

The proportion of disadvantaged pupils - those that are eligible for the pupil premium - in “reverse-gap” schools varies wildly. The proportion is above the national average in 37 per cent of reverse-gap schools; in these schools, 62 per cent of pupils are eligible.

In contrast, in 63 per cent of reverse-gap schools the proportion of disadvantaged pupils is below the national average. In these, just 9 per cent of pupils are eligible. Schools that obliterate the attainment gap therefore tend to serve highly disadvantaged populations, or the extreme opposite.

Partly as a result, reverse-gap schools are not evenly distributed around the country. More than half are located in just four places: 29 are in London, 10 in Birmingham, six in Buckinghamshire and 11 in Kent.

The latter two locations tell a second story: almost half of the gap flippers are grammar schools. So is this a triumph for selection and a reason to bring back the grammars as UKIP have suggested? Probably not. While on average, a comprehensive school with a reverse gap teaches 71 disadvantaged pupils, those that select manage only 11. This is despite the fact that these grammar schools are on average larger than the comprehensives.

Ultimately, it looks like the high-disadvantage, high-equity schools of Birmingham and London have got more to teach us about educational equality than the grammars of Kent and Buckinghamshire. As ever, it is important to be careful who you learn from.

NB: “National averages” are for maintained English schools in 2013 and based on schools for whom complete data was available.