Poland was one of 10 countries to join the EU in 2004
About one million migrants from Eastern Europe have arrived in the UK since 2004 but half of them have already returned home, research suggests.
The Institute for Public Policy Research examined the impact on the UK after the EU expanded in 2004 and 2007.
It suggested that the arrival of migrant workers from 10 countries would also slow, with more returning as conditions in their countries improved.
The migrants had also spread to all parts of the UK to find work, it said.
The research looked at migrants who came from eight of the 10 countries that joined the European Union in May 2004 - Poland, the Czech Republic, Estonia, Hungary, Latvia, Lithuania, Slovakia and Slovenia.
It also included migrants from Romania and Bulgaria, which joined in 2007.
The research by IPPR, a Labour-leaning British think tank, estimated that about one million migrant workers had come to the UK from 2004 accession countries, but that around half of this group had already left the UK.
The IPPR also predicted that fewer migrants from the new EU states would come to the UK and many already in the UK would return to their home countries in the coming months and years.
It based this forecast on the development of the EU countries, with improving economic conditions making it less likely that would-be migrants will leave.
"Four in 10 of the returned Polish migrants we surveyed think that better employment prospects in Poland will encourage Poles living in the UK to return to Poland for good," the IPPR said.
According to the research released to the BBC, there were 665,000 nationals from all 10 countries living in the UK in the last quarter of 2007.
This was an increase of 548,000 since the first quarter of 2004, just prior to the first eight countries joining the EU.
The government had underestimated the number of migrants post-expansion, saying that between 5,000 and 13,000 would arrive after 2004.
In fact, by 2006, Home Office minister Tony McNulty admitted that the government was "in the dark" over arrivals - 293,000 immigrants had applied for work permits in the first 18 months.
As EU countries change their restrictions on the new members, workers will be more likely to migrate there rather than to the UK, the IPPR suggested.
There will also be a smaller pool of possible migrants because of declining birth rates in the mid-1980s.
And the pound's devaluation in relation to the Polish currency will narrow the gap between potential earning in Britain and Poland.
The IPPR said the pound has already fallen by around a quarter relative to the Polish zloty since early 2004.
The research also suggested that the geographical spread of EU migrants in the UK was wider than previous waves of immigration.
It said that even areas that have not traditionally attracted migrants, such as Scotland and south-west England, had attracted a "significant proportion" of migrants.
This showed that migrants were willing to move to where work was available.
The number of migrants from the new EU countries arriving in the UK had also started to slow substantially, with 17% fewer worker registrations in the second half of 2007 than during the same period of 2006, the IPPR said.
"We estimate that some 30,000 fewer migrants arrived in the second half of 2007 as did in the second half of 2006."
The IPPR looked at the Labour Force Survey, national insurance number applications, and the Workers Registration Scheme - applicants are required to register on the scheme as soon as they start working in the UK.
It also studied the International Passenger Survey and questioned Poles who had returned to Poland after working in the UK.
Air travel between Britain and Poland had also changed since accession.
In December 2003 about 40,000 passengers flew between three British airports and Warsaw and Krakow in Poland, but four years later it was possible to fly from 18 British airports to 10 Polish cities.
Passenger numbers between these destinations in December 2007 were almost 385,000.
The IPPR, established in 1988, says it aims to promote social justice, democratic participation and sustainability in government policy through its research and analysis.