Jeremy Corbyn is coming under intense pressure to make a Final Say referendum a condition of Labour support for any Brexit deal, after an exodus of Remain voters consigned the party to its worst national election result since 1910.

The Labour leader is increasingly isolated at the top of the party on Brexit, with senior figures including shadow chancellor John McDonnell, shadow foreign secretary Emily Thornberry and deputy leader Tom Watson calling for a public vote.

Mr McDonnell appeared to accept that the strategy of attempting to straddle Labour’s Remain and Leave-voting constituencies had reached the end of the road.

“Can’t hide from hit we took last night,” he tweeted. “Bringing people together when there’s such a divide was never going to be easy. Now we face prospect of Brexiteer extremist as Tory leader and threat of no deal, we must unite our party and country by taking issue back to people in a public vote.”

He added: “Of course I want a general election. But I realise how difficult this is to secure. I will do anything I can to block no-deal Brexit. So yes if, as likely, general election not possible, then I support going back to the people in another referendum.”

In a message to the Parliamentary Labour Party on Monday, Mr Corbyn sought to reach out to Remainers, stating: “We are ready to support a public vote on any deal.”

But it is understood that the shift of tone and emphasis does not amount to a change in policy to make support for any deal conditional on a second referendum. Mr Corbyn said any policy change would be for Labour’s annual conference in September to determine.

The move did not go far enough for Labour MPs reeling from the party’s collapse to 14 per cent in the European elections, which saw them lose 10 MEPs as voters frustrated with Mr Corbyn’s ambiguous stance on Brexit flooded to Liberal Democrats and Greens.

Emily Thornberry: Labour should have clearly backed Remain during European elections

One Remain-backing shadow cabinet source said that Labour members and supporters demand a commitment to require a public vote on any deal, adding: “Waiting until September won’t satisfy anyone.”

And backbencher Ian Murray, a supporter of the People’s Vote campaign for a second referendum, said: “This is a step forward, but the policy needs to be made very clear and the campaign for a people’s vote needs to start now, not be delayed for any reason. The idea that we should wait until September is ludicrous.

“The one thing the results have shown us is that if you stand in the middle of the road you get hit by both sides. That means those members of the Labour front bench opposing a people’s vote need to recognise that now they need to either get on board or consider their positions. The era of playing both ends against the middle is over.”

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As the disastrous results rolled in on Sunday night, Mr Corbyn appeared to signal a change in strategy, in a statement which said that the Brexit issue “will have to go back to the people, whether through a general election or a public vote”. He said that Labour would “reflect … over the coming days” on the outcome of the European vote.

But in a TV appearance in the morning, he made clear his preferred outcome remains a general election.

“The priority at the moment, I think, is for this government to call for a general election and actually have a general election so we can decide the future,” he said.

Asked whether he would support an internal ballot on the direction of policy, the Labour leader replied: “What we’ll do is consult members through the constituency parties and affiliated trade unions and bring the issue back to conference in September.”

Ms Thornberry said the election results showed Labour was “not clear enough” about its position on Brexit.

“We should have said quite simply that any deal that comes out of this government should be put to a confirmatory referendum, and that Remain should be on the ballot paper, and that Labour would campaign to Remain,” she said.

Meanwhile, shadow home secretary Diane Abbott said Labour must “listen to our members”, who polls suggest back a Final Say vote by a large majority.

“When we come in third after the Brexit Party, that is a clue something is wrong with our strategy,” said the loyal Corbyn ally. “We need to listen to our members and take a clearer line on a public vote.”

Shadow Brexit secretary Sir Keir Starmer said: “It’s no use trying to hide from these very disappointing results. We need to reflect hard and listen to our members, supporters and voters. The only way to break the Brexit impasse is to go back to the public with a choice between a credible Leave option and Remain.”

However, there were indications that some MPs in Leave-backing constituencies will resist any move to position Labour as an anti-Brexit party.