Academics have scotched fears that non English-speaking children hold back British-born youngsters in the classroom.
In fact, in some cases, immigrants were helping drive up standards, the London School of Economics team found.
There have been fears that British-born children were being held back because teachers had to help kids who were struggling with a language barrier.
However, after examining exam results in different primary schools, the LSE said: "The growing proportion of non-native English speakers in primary schools should not be a cause for concern: this trend is not detrimental to the educational attainment of native English speakers."
In the case of Eastern Europeans, there could be extra benefits, the researchers found, with a "small, positive effect in the case of maths."
"We can only speculate as to the possible reasons for this result," the authors of the study ‘Non-native Speakers of English in the Classroom: What are the Effects on Pupil Performance?’ said.
"It may be the fact that immigrants from East European countries are better educated and more attached to the labour market than the native population.
"The children of such immigrants may be a welcome influence in the schools they attend."
This was not enough for traditionalist pressure group the Campaign for Real Education, which denounced the findings and insisted teachers' time was being swallowed up by helping kids who did not have English as their first language.
Its chairman, Chris McGovern, told the BBC: "The fact is that parents will not believe it.
"Many parents come to us and they are very worried that so much teacher time is being taken up with children who can't speak English."
Interview Evan Davies seemed incredulous, saying: "You are talking about standards in education, and you are dissing whole academic discipline and you are saying 'these academics don't know what they are talking about..I know because of common sense'."
A headteacher told the programme: "In all my years of headship, I have never had a parent who came to me complaining about children who do not speak English in the the classroom."