Shadow chancellor John McDonnell said that voters in the local elections had sent a clear message to Labour: “Brexit – sort it.”
And, in an apparent signal that Labour is now determined to bring a resolution to cross-party talks with the Government lasting more than a month over a compromise Brexit deal, he added: “Message received.”
Despite expectations of three-figure gains in council seats which were last contested at a low-point for the party, Labour saw its tally of councillors reduced by 58 overnight and lost control of heartland authorities Bolsover and Hartlepool as well as Wirral.
Visiting Trafford, where the party won overall control for the first time since 2003, party leader Jeremy Corbyn said he was “very sorry” at the scale of losses.
But he hailed positive swings in some areas which he said gave Labour hope of winning marginal seats like Swindon, Peterborough and Thurrock at a general election.
“I wanted us to do better, of course,” said Mr Corbyn. “Results across the country are interesting, to put it mildly.
“But I also say the swings to Labour in many parts of the country show that we can win seats in a general election, whenever that comes.”
A furious internal row broke out over the extent to which Labour is ready to help get Theresa May’s EU Withdrawal Agreement over the line, after shadow cabinet member Barry Gardiner suggested that the party was trying to “bail out” the Tories.
Speaking on an election-night TV panel debate with Brexit minister James Cleverly, Mr Gardiner said: “We are in there, trying to bail you guys out.
“We are now trying to negotiate with you because your Prime Minister, who’s lost control of her party and lost any chance of getting her deal through Parliament, has come to us and said: ‘Please, I now need to listen to the ideas you have been putting forward.’”
And Labour chair Ian Lavery, who has been instrumental in blocking the party from backing a second EU referendum in all circumstances, said the “clear message” from the local elections was that “the two parties need to get on and get Brexit sorted”.
Mr Lavery told the BBC he hoped Labour could “get a deal and exit, as promised in the manifesto”.
Remain-backing Labour MP Wes Streeting tweeted: “Labour should not be bailing the Tories out. Any deal – any – must go to a public vote.
“Without a commitment to a public vote, I’ll vote for a Labour-Tory deal when hell freezes over and I’m not alone in that.”
And Houghton & Sunderland South MP Bridget Phillipson said that the extent of support for Remain among Labour voters even in Leave-backing constituencies like her own was the “elephant in the room” in the debate.
Ms Phillipson said Labour “fudge” over Brexit had played “a key part” in the party’s disappointing performance, with voters in places like Sunderland switching to the Liberal Democrats and Greens.
“Too often, places that voted for Brexit back in 2016 like Sunderland get caricatured by the media as if everyone voted Leave,” she said. “But the majority of Labour voters now want a People’s Vote on Brexit and would vote to stay in the EU given the chance.
“I fear Labour’s position has been too hesitant and lacking in clarity over the past few months, depressing support among our voters at a time when they expect strength and leadership from my party rather than fudge.”
Mr McDonnell said in a tweet: “We’ll see what final results of local elections look like by end of day as they are pretty mixed geographically up to now but so far message from local elections – ‘Brexit – sort it’. Message received.”
But he later backed away from any suggestion that the party leadership were now committed to a compromise deal with the Conservatives, saying his position was that “we need to get on with sorting this out whichever way”.
Remain-backing Labour MP Stephen Doughty responded: “This is just wrong about what most of our party and voters believe. The biggest gains so far are for Liberals and Greens.
“Let me be crystal clear. I will never bail out these disastrous Tories on Brexit. Neither will the overwhelming majority of Labour MPs. We can resolve but not by a backroom stitch-up. We must let the people have the final say on any deal.”
Former minister Chris Bryant said that Labour’s policy of “constructive ambiguity” on Brexit had undermined its chances at the election.
“I never thought constructive ambiguity would survive the white heat of the ballot box,” said Mr Bryant.
“Voters want to know what they’re getting from a party. Fudge just sickens them.”
Labour’s London mayor Sadiq Khan told the Press Association: “What’s important is that before the European elections, we have clarity in relation to our position on Europe.
“In my view, that means giving the British public a final say on whether they accept the deal negotiated by the Prime Minister or the one which has the most support in Parliament, with the option of remaining in the EU.”