Figures studied by data analysts School Dash show that while nationally the number of white non-British or Irish schoolchildren has increased by just 1.2% from 2011 to 2015, some areas have seen an increase of up to 30%.
But while fears have been raised that this might place a strain on teachers, figures show that schools where pupils speak English as an additional language perform better.
The findings will fuel concerns white British children are lagging behind their classmates.
Dr Timo Hannay, founder of School Dash, told the Press Association: “Nationally there doesn’t seem to be a huge change over that period, but locally in some areas and some particular schools, there can be. It is a very location-specific phenomenon.
“You get some locations where it is 30% of the population, and obviously that is huge. But it is highly localised, it is not only location specific, it can be very school specific as well.
“On the whole those schools that have large numbers of non-British white pupils tend to do better than schools that have a smaller number of them.”
The report aims to shed light on the impact EU expansion and immigration has had on Britain’s schools ahead of the referendum later this month.
Dr Hannay, the report’s author, said there are no national statistics for the number of British school pupils from the EU, so he used figures for white non-British and non-Irish children to give an approximate picture.
The figures show that London, Peterborough and parts of Lincolnshire and Norfolk have had the biggest influx of EU immigrant children enrolling in its schools.
The report found that schools with high white immigration did better than their low white immigration rivals, although this was mainly the case in London and outside the capital there was little, if any, difference.
It stated: “This may seem surprising. Why would schools with large numbers of foreign kids, many of whom learned other languages before picking up English, do better academically than similar schools catering mainly for native British pupils?”
Dr Hannay said the difference may be because immigrant families value education more than British natives.
He said: “Educationists tend to see having English as an additional language as a positive indicator of educational outcomes because a lot of those immigrant communities take education incredibly seriously.
“So even though the child may not have learnt English as a first language, they still may be adept at it and on the whole they seem to do better at school.”
He added: “The increase in performance seems to be a London-specific effect. Why is that? There are two hypotheses and I suspect they are both a little bit true.
“One is that London is better at assimilating and educating those kind of children, it has got a very diverse population and its schools in recent years have got quite good, and maybe London for one reason or another is a better environment for those kids to thrive.
“The other is that it may well be that the better educated and more aspirational immigrant families tend to end up disproportionately in London than in other areas.”