British support for staying in the European Union has tumbled over the past four months as an influx of migrants into Europe has pushed many voters towards opting for an exit, the Ipsos MORI pollster said on Thursday.

Prime Minister David Cameron is seeking to renegotiate relations with the bloc it joined in 1973 ahead of a referendum on membership by the end of 2017.

In one of the starkest illustrations to date of how the migrant crisis may be polarising British views of Europe, an Ipsos MORI poll showed 52 per cent of Britons would vote to stay in the EU, down from a record 61 per cent in June.

Support for a British exit rose to 39 per cent, the highest level since 2012, up from 27 per cent in June. That more than halves the "in" lead to 13 percentage points from 34 points in June.

"We know that immigration has been the big issue over the summer and that has been partly driven by all the stories about migration from Syria and other places into Europe and the refugee crisis," Gideon Skinner, head of political research at Ipsos MORI, said by telephone.

"This is part of what is driving this," he added.

Cameron has said that he wants to argue for Britain to stay inside the EU if he gets the changes he wants from other European leaders.

But British public opinion on Europe is volatile: In 2012, Ipsos polling showed more Britons wanted to leave than stay. That has since switched around but polling shows immigration is now voters' top concern.

A British exit would shake the Union to its core, ripping away its second largest economy and one of its top two military powers.

Pro-Europeans warn an exit from the EU would hurt Britain's economy and could trigger the break-up of the United Kingdom by prompting another Scottish independence vote, while opponents of EU membership say Britain would prosper outside.

Over half of Britons said they could be persuaded to change their mind about membership.

Until Cameron has a deal, his government is refusing to back either the domestic "in" or "out" campaigns which launched over the past few weeks.

The most popular of Cameron's proposed changes include bringing powers back to Britain, restricting free movement of labour and cutting benefits for EU migrants.

Just 37 per cent of voters are confident he will secure a good deal, Ipsos said.