International students contribute an eighth of university revenues, according to new analysis.
Research also found no evidence that the presence of school students with English as an additional language affects the performance of classmates whose first language is English.
The share of higher education institutions' income that came from non-EU student fees grew by two thirds from 7.7% to 12.7% between the 2005/6 and 2014/15 academic years, the Migration Observatory at the University of Oxford said.
Tuition fee income from non-EU students was £4.2 billion in 2014/15, figures show.
Another briefing examined data and evidence on school pupils in England with English as an additional language (EAL), which includes both children who have moved to the UK from overseas and those born in the UK.
It found that they have lower achievement on starting school, but this effect reduces markedly with age and is largely eliminated by 16.
The study said: "There is currently no evidence that EAL students negatively affect the attainment of those with first Language English."
Madeleine Sumption, director of the Observatory, said: "Migration has clearly had an enormous impact on the composition of school pupils in the UK, particularly in London.
"This presents a logistical challenge for schools and local authorities, but so far there is no evidence that the outcomes that ultimately matter most—the performance of children in schools—have been affected."
She added: "It is still too early to forecast the migration-related impacts the UK's decision to leave the EU on the UK education system.
"We will not know for some time how and whether migration policies will change, which makes planning ahead difficult."