Jeremy Corbyn is under pressure over an explosive claim that he broke a pledge to support a new Brexit referendum if Theresa May rejected his compromise plan.

A letter from the Labour leader to the prime minister – setting out five legally binding demands as his price for backing a deal – angered many Labour MPs by making no mention of a fresh public vote.

Now it has been alleged that Mr Corbyn’s office agreed the letter should set out clear support for the referendum, if Ms May turned down his offer, only to omit the sentence at the last minute.

Mr Corbyn’s office declined to comment on the claim, although a Labour source told The Independent the allegation was “false”.

Labour MPs backing a Final Say people’s vote urged Mr Corbyn to come clean about what commitments were given about the contents, before it was sent last Wednesday.

“Time after time, Labour members and supporters demand a people’s vote. Yet time after time, this is thwarted from the top,” said Chris Leslie, Labour MP for Nottingham East.

And Ben Bradshaw, MP for Exeter, said: “If true, any attempt by the leadership, or figures in the leader’s office, to subvert or renege on Labour’s unanimously agreed policy would provoke uproar among our members, voters and MPs.”

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The claim has been made by Robert Peston, ITV’s political editor, who said “multiple sources” told him the Labour leader’s office went back on the commitment given to Keir Starmer, the party’s Brexit spokesperson.

Sir Keir had “agreed that the final part of Corbyn’s letter to May would say ‘if you do not accept this [Brexit offer] there will be a people’s vote’,” Mr Peston claimed.

“LOTO [the leader of the opposition] agreed to this. But then Keir discovered after the letter had been sent and published that the people’s vote paragraph had gone.”

Both Sir Keir and Mr Corbyn’s spokesperson declined to comment on the claim concerning the pair’s private discussions.

Mr Corbyn was forced onto the back foot after the letter, and quickly assured Labour MPs and members he was not ruling out a further referendum.

John McDonnell, the shadow chancellor, went further – saying Labour wanted a compromise “in the national interest”. He added: “If we can’t do that, well yes, we have to go back to the people.”

Crucially, Downing Street has now firmly rejected the central plank of Mr Corbyn’s compromise plan, namely the UK being part of a permanent customs union.

The prime minister’s spokesperson said: “We are absolutely clear on this – we’re not considering Jeremy Corbyn’s customs proposals.

“We’re not considering any proposals to remain in the customs union. We must have our own independent trade policy.”

David Lammy, another Labour MP supporting a fresh referendum, said the letter showed Labour must now start “campaigning for a people’s vote”.