European expansion has boosted the UK economy and put it in a strong position to cope with growing globalisation, a committee of peers has said.
Romania will join the EU in January
Immigration from 10 new EU countries since 2004 has meant the influx of a skilled, low-cost workforce, it added.
But while experts back EU expansion, there is growing public opposition, the Lords EU Committee report said.
It urged EU leaders, some of whom had their own "hostile and ambiguous" approach, to champion enlargement.
The committee's report found the UK had benefited from its "open-door" policy towards migrant workers in 2004.
The government has imposed restrictions on the rights of unskilled Bulgarians and Romanians to work in Britain, when those countries join the EU in January.
The report pointed out that in EU countries which imposed restrictions in 2004, many workers simply joined the black economy.
"In a global economy, where competitiveness is key, immigration from eastern Europe has helped British companies compete with those in the emerging economies of Asia," said committee chairman Lord Grenfell.
The report concluded that the effect on the EU of previous enlargements had been "broadly positive".
But it noted that many western Europeans felt the prospect of cheap labour threatened their jobs.
And the perception of countries from the Balkans or the former Soviet Union as being "poor, politically unstable and ridden by problems of organised crime" had fuelled opposition.
The committee drew attention to opinion polls which suggest that, although more Europeans support EU enlargement than oppose it, the gap is narrowing.
In Germany, France and Austria more than 60% of people polled in spring 2006 opposed it.
The report said a larger EU would need institutional changes to function effectively.
However, it argued against the idea - put forward in September by European Commission President Jose Manuel Barroso - that there should be no further enlargement until institutional changes had been agreed.
The peers said "an artificial 'pause' ... would be destabilising for applicants and could become a trap from which it would be difficult to emerge".
All applications should continue to be handled on their merits, in a measured way, they said.
They added the countries of the western Balkans - Croatia, Macedonia, Serbia, Bosnia and Albania - were "fragile and fractious" and could return to sectarian violence without the prospect of EU membership.
They recommended that governments should acknowledge that the constitution - which was rejected by French and Dutch voters in 2005 - will not be adopted in its current form.