Voters believe Brexit will bring immigration under control but hit them in the pocket – and 54 per cent now back Remain, a major poll has found.

The survey of 20,000, the largest since the 2016 referendum, found a swing away from Leave, with respondents saying they would now back staying in the EU by 54 per cent to 46 per cent. The referendum saw 52 per cent vote Leave.

Survation’s poll for Channel 4 News found support for Brexit has declined sharply in some constituencies which were staunchly pro-Leave two years ago.

Researchers found the number of local authority areas backing Brexit has fallen from 262 in the referendum to 157 today. The number backing Remain has risen from 116 to 221.

Pictured: Theresa May speaks during a media conference at an EU summit in Brussels last month

The results of the Survation poll of 20,000 for Channel 4 News are shown in this graphic

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Double-digit falls in support for Brexit were recorded in a string of seats in Labour’s heartlands, including Wigan, Stoke-on-Trent and Middlesbrough.

The findings could help sway the mood of Labour MPs as they consider whether to back Theresa May’s Brexit deal or join the campaign for a second referendum.

The map shows in blue the areas projected to vote Brexit in the event of a second referendum held today

The poll did not, however, find conclusive backing for yet another vote. Some 43 per cent said they would support a referendum that pitted a final Brexit deal against remaining in the EU – but this was opposed by 37 per cent.

Fewer than one in six (16 per cent) believe Brexit will be good for their own finances, with 38 per cent braced for a negative impact.

Prime Minister Theresa May (pictured here at an ASEM leaders group summit in Brussels last months) is still trying to secure a final Brexit deal with the European Union

Respondents were more bullish on the economy as a whole, with 31 per cent predicting Brexit would be good for UK plc – although almost half (44 per cent) said our break from Brussels would be bad for Britain’s bottom line.

Four in ten said leaving the EU would be good for levels of immigration, while more than a third said they would not be concerned if Northern Ireland left the United Kingdom.

Former Ukip leader Nigel Farage said: 'Funny isn't it? On the one hand we are being told Brexit has made people hostile towards migrants, on the other we are told we are more relaxed about it.

Former Ukip leader Nigel Farage (pictured) questioned the narrative that Brexit had made people hostile to migrants

'You can't have it both ways. The truth of it is, the reason those figures have changed is a big chunk of the electorate think the immigration issue has been dealt with because we voted Brexit, and they think our major political parties will carry out their wishes.

'Actually, the penny's not yet dropped. That there is no intention for this Government or this opposition to deal with open door immigration.'

In a no deal scenario, a majority of voters would back staying in the EU, at least temporarily, according to the poll.

The survey found that in a no-deal situation 35 per cent believe Britain should remain in the EU, while 19 per cent would want to delay leaving to allow more time for talks, and 36 per cent would wish to quit the bloc.

It also asked how people would vote if the government secured a deal tomorrow, with the question being predicated on the assumption that the agreement would reflect what has been seen from Number 10 so far.

Most said they would reject such a deal - 33 per cent - as 26 per cent responded they would accept it, 34 per cent did not know and seven per cent indicated they would not vote.

The poll divided viewers online, with some remarking on the supposed pro-Remain agenda of Channel 4 and others praising the power of the research.

Justice Secretary David Gauke last night said: ‘We are at the end of a negotiation, in a period where there is a lot of uncertainty. I am not at all surprised there has been a swing to Remain. If we get a deal there could be a swing back to Leave.’

Labour’s shadow international trade secretary Barry Gardiner said he was ‘heartened’ by the responses to Survation, which conducted its poll online across every constituency in the UK between October 20 and November 2.

Respondents were also asked if they thought Boris Johnson, Jeremy Corbyn or Nigel Farage would be handling Brexit negotiations better than Theresa May.

Mr Farage came off worse, with 48 per cent saying he wouldn't be doing as good a job as the prime minister. A total of 45 per cent of those surveyed said the same about the Labour leader and 46 per cent said Mr Johnson would be worse at negotiations too.

The survey also raised the possibility of a deadlock in negotiations and what they UK should be willing to agree to if such a situation occurred.

It found the most unpopular prospect to be Britain agreeing to limitations on trade with non-EU countries, as 62 per cent said the government should not agree to limitations even to break a deadlock.

A total of 45 per cent of respondents also rejected the notion of checks on goods crossing the Irish Sea between Northern Ireland and the rest of the UK.

The one notion that respondents said the government should be prepared to agree to in order to break a deadlock was that after Brexit UK and EU citizens should be free to live and work in each other's countries - with 63 per cent backing the prospect.

Adherence to EU regulations on manufactured goods was backed by 50 per cent in the event of a deadlock, but 32 per cent rejected the idea and 19 per cent were unsure.