Britain's Cameron wants labour curbs for any new EU members

* Cameron under pressure to limit access to UK labour market

* PM fears being outflanked by anti-immigration party

BRUSSELS, Dec 20 (Reuters) - Britain will push for tougher accession terms for any new members of the European Union to limit their citizens' access to the bloc's labour markets, Prime Minister David Cameron said on Friday.

Cameron is under pressure to limit foreigners' entry into to the British labour market and has unveiled a series of measures to stop EU migrants being able to claim welfare benefits as soon as they arrive in Britain.

Immigration is a particularly sensitive issue in Britain, where many eastern Europeans, including Poles, Hungarians and Czechs, have come to work following their countries' accession to the EU in 2004.

Surveys show, however, that the influx of eastern Europeans has added to British gross domestic product and that they contribute more to social security coffers than they take out in welfare payments.

Speaking at an EU summit where the bloc's governments confirmed plans to start membership talks with Serbia next month, Cameron said admitting new countries should not be allowed to lead to "big movements of population".

"We have to learn the lessons of history. Enlargement has been a success. Transitional controls have been a success," he said. "We need to go one step further and have more robust transitional controls in the future."

Cameron's Conservative party is trailing in opinion polls ahead of a 2015 election and surveys showing most Britons don't want the labour market to be further opened up to east European workers.

Popular (NasdaqGS: BPOP - news) newspapers are focusing on what they see as a pending influx from Bulgaria and Romania at the beginning of 2014 when transitional curbs on those countries end.

Anxious not to be outflanked by the anti-EU, anti-immigration UK Independence Party (UKIP), Cameron has said he shares public concerns about the end of restrictions on Romanians and Bulgarians working in Britain.

The two Black Sea states joined the EU in 2007, and Croatia became the EU's 28th member last year. But it will likely take at least a decade before any new countries are admitted.

Other than Serbia, four more countries are candidates for accession: Iceland, Turkey, Montenegro and Macedonia.

Free movement of people is one of the EU's main tenets but Europe's economic crisis has sparked numerous attempts to limit how citizens and immigrants can travel and work in the EU. (Reporting by Justyna Pawlak and Robin Emmott)