LAST year’s free school meal figures for England and Wales reveal the first significant increase in the polarisation of school intakes in 10 years.

Between 1989 and 1998 the socio-economic gap between schools gradually narrowed. But the 1999 statistics suggest that this improvement is now ending.

Although segregation assessed by other indicators continues to fall year-on-year, this recent development should, in our opinion, have been the focus of the Analysis article, “Market proves a divisive force” (TES, March 17).

We have calculated changes in the social composition of all state primary and secondary schools in England and Wales by using various indicators of disadvantage. These include not only eligibility for, and take-up of, free meals but ethnic group, special needs, first language and level of proficiency in English.

Our measure of segregation is the proportion of pupils who would have to change schools for each indicator to be evenly distributed. This measure, used previously in sociology, economics and geography, has a pedigree going back to work done in the United States on ethnic segregation in the 1950s.

Several comments reported in the March 17 article are false. We do not attribute changes in segregation to “market forces”. We simply reported that we have not discovered the rise in segregation since 1988 that other writers had predicted. This does not make our findings either “flawed” or “dangerous”.

We do not intend to use the columns of The TES to trade insults with the Exeter researcher who levelled these accusations at our work. What we will say is that researchers at the London School of Economics and Lancaster University who have used the datasets we analysed have recently produced findings that are in line with ours.

Like us, they have discovered that, untl recently, patterns of segregation were decreasing nationally, but with substantial local variation. (Incidentally, although the LEAs with the greatest increase in segregation were referred to in The TES article as the “worst” this description did not come from our work.)

It is local variation that makes smaller-scale studies risky. The work by the Exeter team that was said to be in opposition to ours suffers from this. Their findings are based on 300 schools (the top and bottom 10 per cent of 1,500 schools) whereas our findings are based on direct evidence about the intakes of 23,000 schools over 11 years.

However, one significant trend has been confirmed by both the Exeter study and previous larger national analyses - the performance gap between the top and bottom schools in England and Wales is reducing over time. The Exeter researchers do not accept this, but that is what their figures show.

In 1994, the top 10 per cent of the 1,500 schools included in the Exeter survey had a “benchmark figure” (the percentage gaining five or more GCSEs at A*-C) of 65 per cent whereas the equivalent figure for the bottom 10 per cent of schools was 10.4 per cent. The corresponding figures for 1998 were 70.9 per cent and 12.8 per cent.

This means that there was a gap of 72 per cent in 1994 but by 1998 this had narrowed to 69 per cent (we arrived at these figures by using a standard method of assessing gaps such as that advocated by the Equal Opportunities Commission and examination boards).

Of course, the gap is still large and there is no suggestion that any of us should rest easy with such a polarised education service, but the point is that by any sensible arithmetical calculation, the school system has been moving in the “right” direction. It is this fact that makes our new finding of a possible reverse in the trend so important.

The Cardiff University research has been carried out by Stephen Gorard, John Fitz, Chris Taylor and Patrick White