There are 1.1million Muslim immigrants and 1.3million UK-born Muslims – mostly the children of newcomers.
Muslims quizzed said there was less open hostility to Islam in Britain than other EU countries and that the Government is sympathetic to them.
But critics seized on the findings as confirmation that Labour’s multicultural policies are pandering to Islam.
Sir Andrew Green, of the pressure group Migrationwatch, warned the Muslim population in Britain was likely to be even higher than research showed.
He said: “The rapid rise in the Muslim population is just one way in which mass immigration promoted, even encouraged, by this Government has affected the whole nature of our society.”
Muslim illegal immigrants were unlikely to respond to Government-linked surveys, he added.
The population research is to be published next month in a new “faith map” of the UK drawn up by the Institute for Public Policy Research, a think-tank with close links to 10 Downing Street.
Even the authors admit the increasing numbers of immigrants of different religions will be “challenging” for social cohesion in the UK. The report found in the past decade a rise of 275,000 in the number of Muslims who were born in Pakistan or Bangladesh living in Britain.
The increase is equivalent to twice the population of Oxford.
And the number of Somali-born UK residents had also risen sharply – from fewer than 40,000 in 1999 to 106,700 this year.
They claimed to prefer the UK because of “latent Islamaphobia” abroad, the report said.
The “faith map” showed that 4.5million immigrants living in Britain had a religious affiliation.
Of those, around a quarter were Muslim and more than half Christian. Polish Catholics and African Pentecostals also were also among the fastest-growing religious communities in the UK.
The findings were based on previously unpublished results of the Labour Force Survey, which quizzes 200,000 people each year.
Researchers said traditional church attendance had declined over the last decade but evangelical Christianity was growing.
The report, called Faith, Migration and Integration in the UK, says: “A challenging change is that brought about by the arrival of migrants with an established faith organisation whose traditions and beliefs differ from that of the UK-born population.”
A separate report found British Muslims are the most patriotic in Europe. Seventy-eight per cent think of themselves as British, says the Open Society Institute. In Germany it was 23 per cent.