Vote Leave are attempting to exploit "deep splits" among the Remain campaign over immigration, arguably the top issue in the EU referendum alongside the economy. The Brexit backers have seized upon Theresa May's latest remarks, which saw the pro-EU Home Secretary call for further reforms from Brussels over free movement of people rules.

"There are some changes coming up in free movement rules, to make it easier for us to deal with illegal immigrants and I think again as I've said that we should look at further reform in the future," the top Conservative told the BBC. The comments contrast with Chancellor George Osborne, who has ruled out any immediate immigration reforms from the EU.

Labour's leadership have also clashed over the issue, with Jeremy Corbyn pledging to defend the political and economic bloc's free movement of people principle after deputy leader Tom Watson suggested the EU's rules may have to be revised. "It's intrinsic to the European Union that there has to be free movement of people," Corbyn told BuzzFeed.

Vote Leave, who have backed an Australian-style points system, have subsequently branded the Remain campaign as a "complete mess". Matthew Elliott, the chief executive of the Brexit group, added: "Not only are they divided over whether or not to talk about immigration, they are deeply split when they do.

"David Cameron and George Osborne are adamant that there is no need to change the freedom of movement rules, while the Home Secretary says that they need reform. Jeremy Corbyn can't agree with his own deputy Tom Watson. No wonder the public don't trust the Government's commitment to bring migration down to the tens of thousands."

The latest issues index from Ipsos MORI, of more than 900 people between and 6 and 15 May, put immigration as the UK electorate's top concern (38%), with NHS/hospitals second (33%) and the EU/Europe third (28%).

David Cameron had promised to cut immigration levels down to "tens of thousands", but the latest figures from the Office for National Statistics (ONS) showed net migration to the UK climbed to 333,000 in 2015.

Meanwhile, the latest opinion polls have the EU referendum campaigns almost neck-and-neck. The latest online survey from ComRes for The Sun, of more than 1,000 people between 9 and 13 June, put Remain on 46% (-6) and Leave on 45% (+4), with 9% of respondents undecided.