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Labour could haemorrhage nearly a third of its 2017 election support to the Liberal Democrats and Greens in London and the South East over its Brexit policy, according to internal research.

Leader Jeremy Corbyn has committed the party to a second referendum if it wins power, with a choice between a newly negotiated Brexit deal or Remain — but he has stopped short of saying which side it would back.

The Standard has been told that internal Labour/union research suggests such a stance risks just over 29 per cent of the 2017 Labour vote in London going to the Lib Dems and Greens, unequivocal Remain parties, compared with 9.4 per cent to the Conservatives and Brexit Party, who want to Leave.

These swings could mean Labour failing to win the Remain stronghold of Putney from the Tories.

Its chances of holding Hornsey and Wood Green, where the Lib Dems are the main challenger, and Hampstead and Kilburn, where a Lib-Dem surge could allow the Tories to regain the seat, would also be put at risk.

The picture is even more stark in the South East, where nearly 34 per cent of Labour backers two years ago could switch to the Lib Dems or Greens, and slightly more than 11 per cent to the Tories and Brexit Party.

This would appear to make it very difficult for Mr Corbyn’s party to hold on to seats such as Canterbury or to take constituencies such as Hastings and Rye, currently held by former Cabinet minister Amber Rudd.

Nationwide, just over 30 per cent of the Labour vote could shift to the Lib Dems or Greens, according to the analysis, and slightly more than 12 per cent to the Tories or Nigel Farage’s party.

Labour is believed to be at risk of losing dozens of seats across the country, though so-called “Bolsover Leavers”, named after Bolsover Labour MP Dennis Skinner who is loyal to Labour despite the Brexit issue, will make some less vulnerable.

Other internal polling may be less grim for Labour but overall it is struggling in the polls, with at least one showing the party behind the Lib Dems.