Workers from new EU countries seeking UK jobs is down, says Mr Woolas
Britain could have the biggest population in Europe by 2050 and be the third biggest recipient of migrants in the world, UN projections suggest.
They predict net immigration will average 174,000 a year up to 2050, swelling the population to 72 million.
The US would take the largest number of migrants - 1.1m a year between 2010 and 2050. Canada would take 214,000 a year.
A minister said earlier that numbers of workers from new EU states applying to work in the UK were falling.
The UN predictions, based on the latest census and research from around the world, suggested Britain would be the third biggest recipient of immigrants between 2010 and 2050.
After the US, Canada and Britain - Spain is projected to take 170,000 migrants a year, Italy 159,000, Germany 110,000, France and Australia 100,000.
It would mean by 2050, Britain would have a population of nearly 72.4 million - overtaking Germany, whose population is projected to fall sharply over the period, as Europe's largest country.
Although Germany's population is currently above 82 million, the UN suggests a combination of falling birth and rising mortality rates could see this drop to about 70 million by 2050.
The researchers said the global economic crisis would only slow down migration rates temporarily.
Labour MP Frank Field and Conservative Nicholas Soames - who campaign on the issue of immigration - said it was "more evidence of the pressure that uncontrolled immigration will place on our population, and therefore our quality of life".
The Conservatives said it was evidence of the need for "proper controls" on immigration - including a cap on work permits and language test for those who want to move to Britain to get married.
Earlier, Immigration Minister Phil Woolas told MPs on the European Scrutiny Committee the "best estimate" of numbers of workers from the 10 newest countries to join the European Union was a prediction of 665,000 for next month - 550,000 more than when they joined the EU in May 2004.
The estimates were based on registration figures, data from the Labour Force survey and analysis by the Institute for Public Policy Research.
But he told the committee that the numbers of people applying for the Worker Registration Scheme - which residents of the accession countries have to join if they want to work in the UK for more than a month - were falling.
In the final quarter of last year, 29,000 had applied, compared with 53,000 in the same period on 2007 and 65,000 in the last three months of 2006.
Mr Woolas said this was mainly explained by a fall in the numbers of applications from Polish nationals.
On Monday, Business Secretary Lord Mandelson told the committee that eastern Europeans were filling jobs that British people did not want to do and had made a "positive contribution to the UK economy as a whole".
Mr Woolas said the Home Office agreed that there had been a "general value added" from the migration of eastern European workers.
But that did not mean it could be "extrapolated into the future".
The government has until the end of April to decide whether it wants to extend the Worker Registration Scheme for eight of the accession countries - excluding Romania and Bulgaria - until 2011.
It began phasing in a new immigration points system, which is based on education, previous salary and age, last year, for migrants from outside the EU.