India was in the third place in 1951, with many of those coming to Britain as the children of service personnel who were based in the country before independence in 1947, an analysis of the 2011 census reveals.
It also found that immigration accounted for almost half the increase in the population in England and Wales over the past 60 years.
Since 1951, historical immigration from the Republic of Ireland was followed by large numbers from India, Pakistan, Jamaica and Poland.
Downing Street announced a ban on EU immigrants claiming state benefits until they have been in Britain for at least three months as a means to address concerns that many would come into the country simply to access state-sponsored allowances.
"I want to send the clear message that whilst Britain is very much open for business, we will not welcome people who don't want to contribute," Prime Minister David Cameron said here today.
British ministers have declined to say how many people they expect to come to the UK following the lifting of controls but Bulgarian officials say they expect about 8,000 of their citizens to make the move every year.
Pressure group MigrationWatch UK says the figure will be much higher and it expects 50,000 people to come from Bulgaria and Romania each year for the next five years.
EU rules allow benefit recipients to receive payments from their home country for three months when they move.
Those wishing to do so have to fill out a form authorising the "export" of their benefits.
However, those staying longer than three months in another country without finding a job or getting an extension will lose their entitlements.
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