The findings of the opinion poll conducted by Mori will come as an embarrassment to ministers, after Alan Johnson, the Home Secretary, ruled out imposing a cap.
Just 13 per cent of those asked for their views on whether a “strict limit” on immigrant numbers should be introduced said that they opposed the move. Another 81 per cent were in favour, according to the poll by Ipsos MORI for the UK Border Agency.
There was also a sharp increase in the number who feared that immigration could have an impact on their own job prospects.
More than two-thirds of those surveyed, 69 per cent, said that they considered immigration to be a big or fairly big problem. Among this group, there was a 20 per cent increase since the start of the recession in the number who considered that their position was at risk from immigrants.
Two-thirds of respondents described themselves as fairly or very dissatisfied with the Government’s handling of the issue of immigration, with a slightly smaller number, 64 per cent, saying that laws should be tougher.
Earlier this month, Mr Johnson told MPs on the Home Affairs Committee that he did not “lie awake at night” worrying about the prospect of the population hitting 70 million.
Campaigners claim that millions of new arrivals could flood into Britain, forming 70 per cent of the nine million increase in the population which they predict by 2028.
Ministers say that the new Australian points system allows in only skilled immigrants who benefit the country financially.
Mr Johnson told the committee that a cap would harm the economy, adding that Britons should “welcome” immigrants who came to live and work here, and that he was “happy” to live in a multicultural society.
He went on: “I do not lie awake at night worrying about a population of 70 million.
“I’m happy to live in a multicultural society. I’m happy to live in a society where we not only welcome those coming to live and work in this country, but also where we can go and live and work in other countries.”
Mr Johnson said the argument that immigration had made a contribution to the economy was “irrefutable”.
But, he added: “The argument gets more difficult when you get into hard economic times.”
– Ipsos MORI polled 1030 people aged 16 or over between February and March this year.