Labour has admitted that the party’s unity over Brexit has been “fraying around the edges” after 14 MPs defied the party whip in a vote that delivered a victory to Theresa May.

A handful of shadow ministers also abstained in the vote which meant the prime minister blocked a bid to delay Brexit past the UK’s 29 March departure date.

Jeremy Corbyn’s spokesman said that rebels would be “dealt with by the whips” in the usual way following the split exposed by the vote, but Remain and Leave factions of the party criticised each other in public in the wake of the vote.

It comes as Mr Corbyn met the prime minister in Downing Street to discuss the country’s future path, where he planned to make the case for a permanent customs union and close relationship with the single market.

Mr Corbyn’s backing for the amendment laid by Yvette Cooper was expected to allow it to pass through the Commons on Tuesday, which would potentially have forced Ms May to delay Brexit for up to nine months.

But 14 of the Labour leader’s own MPs defied the whip and voted with the government, with most of the rebels representing constituencies that voted Leave in the 2016 referendum. Several members of his frontbench also dodged the vote.

The spokesman denied the leader’s office had given a “nod or a wink” to MPs from Leave-supporting constituencies that they could safely defy orders over the issue to preserve local support.

Asked how Mr Corbyn would respond to the rebellion, his spokesman said they would be “dealt with by the whips office in the usual way”, without giving more detail.

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But he added: “There will be some fraying around the edges, but we’ve kept the party united both externally and internally.”

Mr Corbyn himself later said he was “disappointed” that some Labour MPs had voted in favour of the Brady amendment, allowiung Ms May a mandate to keep negotiating on her deal, on Tuesday night.

“I’m very disappointed of those that chose to vote with the Conservatives last night on those issues.”

Asked if he would take disciplinary action against MPs who rebelled, he said: “We will be having discussions with them.”

Remainers within the Labour movement, and also some close leftwing allies of Mr Corbyn, attacked the rebels for “riding to the rescue” of the PM.

MPs vote on Brexit plans: Which amendments passed

Senior MP Chuka Umunna – a champion of the People’s Vote campaign – said he was “angry” and disappointed at the Cooper amendment’s failure to pass.

There were calls from some Corbyn allies for MPs to be deselected. Commentator Paul Mason tweeted: “Withdraw the whip, expel from the Labour party and select socialists instead of xenophobes.”

The group who rebelled included veteran left-winger Dennis Skinner, Caroline Flint, John Mann, Graham Stringer and Kate Hoey. Hitting back, Mr Stringer likened MPs who were trying to delay the UK’s exit from the European Union to “kindergarten” children.

He said: “Often in discussing the European Union my colleagues use kindergarten language, they say ‘they’re our friends, how could they not have our interests at heart?’

“I think it misunderstands that actually the bureaucrats in Brussels are a self-interested group of people, self-interested in their own survival and perpetuating their growing power and influence across the whole of the European continent.”

The MP for Blackley and Broughton said “shop steward trade unionists” would not enter negotiations with the managers by saying “whatever you do, we won’t go on strike”, as he criticised the approach to take a no-deal exit off the table.