Official 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 per cent from 2011 to 2015, some areas have seen an increase of 9 per cent.
Dr Timo Hannay, who wrote the new report, said: "Nationally there doesn't seem to be a huge change over that period. It is a very location-specific phenomenon.
"You get some locations where it is 30 per cent of the population, and obviously that is huge. But it is highly localised...it can be very school-specific as well."
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 generally perform better.
The findings will fuel concerns that white British children are lagging behind their classmates.
"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," Dr Hannay said.
The new report aims to shed light on the impact European Union (EU) expansion and immigration has had on Britain's schools, ahead of this month's Brexit referendum.
Taking education seriously
Dr Hannay said there are no national statistics for the number of pupils in British schools from other EU countries. He therefore used figures for white non-British and non-Irish children to give an approximate picture.
The figures suggest that London, Peterborough and parts of Lincolnshire and Norfolk have had the largest influx of EU immigrant children to their schools.
The research shows that schools with high numbers of white immigrant pupils did better that those with few white immigrant students. However, this was primarily true in London; outside the capital, there was little, if any, difference.
The report states: "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 could be explained by the fact that immigrant families value education more than some British native families.
He said: "A lot of those immigrant communities take education incredibly seriously. So, even though the child may not have learned English as a first language, they still may be adept at it."
He added that he had two hypotheses to explain the fact that the gap in performance was concentrated in London.
"One is that London is better at assimilating and educating those kind of children," he said. "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."