More than three-quarters of British people want to see a cut in immigration, a survey of social attitudes has revealed.
However, fewer people now than in 2011 think immigration is bad for the economy - 47% in 2013 compared with 52% two years previously, new findings from NatCen Social Research's British Social Attitudes survey found.
The latest results of the survey, which are to be revealed in a BBC Two documentary The Truth About Immigration tonight at 9.30pm, come nearly a week after access restrictions to the UK labour market were lifted for Romanians and Bulgarians.
Penny Young, chief executive at NatCen Social Research, said: "British Social Attitudes shows that public desire for a cut in immigration to the UK had begun to rise even before the restrictions on migrants from Romania or Bulgaria were lifted at the start of the year.
"Moreover, a majority of people who think immigration is good, economically or culturally, for the UK still want to see it cut.
"These findings highlight the complexity of this issue for politicians facing two elections in 18 months and with limited options if they want to attempt to reduce migration from Europe.
The research shows 54% of respondents see immigration as good for the economy and 55% of those who see it is as culturally beneficial also want to see immigration reduced.
The survey also reveals divisions among political party supporters.
Some 40% of Labour party supporters think immigration is bad for the economy but 36% believe it is good for the economy, the research shows, while 40% think immigration is bad for British culture and 41% see it as good for British culture.
Meanwhile, some 52% of Conservatives believe Britain's cultural life is undermined by immigration into the UK compared with 20% of Liberal Democrats.
Immigration is least popular among people with few or no qualifications, NatCen said.
A total of 85% of those with few or no qualifications want to see a decrease, while 88% of people in higher grade manual jobs want a reduction.
In the documentary, presented by political editor Nick Robinson, former Labour ministers reflect on their decision to open the doors to workers from Eastern Europe in 2004, when Poland and seven other countries joined the EU.
Jack Straw, foreign secretary from 2001 to 2006, said: "The predications were completely catastrophic. I mean they were wrong by a factor of ten. On immigration, it was bluntly a nightmare and it got more and more difficult."
"We did get it wrong and I deeply regret it," said Mr Straw. "I regret it because it undermines trust in government, if you're that wrong."
But David Blunkett, home secretary from 2001 to 2004, told the programme he did not regret the decision.
He said: "I'm unapologetic because if you don't have legal managed migration and people don't sign up so they pay national insurance and tax, they'll work illegally."
Theresa May, Home Secretary, told the programme: "I think the problem in the past has been that there's been this general assumption that immigration was always good for the economy.
"I don't think people have looked at it sufficiently closely to be able to recognise the impact it has on members of the public."
Shadow home secretary Yvette Cooper said: "I think there should have been more debate about immigration, I think we should have had a more calm, measured debate and sensible response to people's concerns, but also listening to what those concerns were, listening to people who were worried about jobs or wages or worried about the pace of change.
"And to have that debate about it rather than simply thinking you can't talk about it for fear that that might be the politics of the Right."
UKIP leader Nigel Farage told the programme that he believed that fear of being labelled as a racist has stifled the debate on immigration.
He said: "They tried to rubbish us, they tried to say that anybody that dared to talk about this subject was necessarily a bad person and racist, that was what they tried to do and actually this has been going on ever since (Enoch) Powell's speech."