Labour MPs who back staying in the EU single market have vowed to keep the pressure up on the government and their own leadership in the Brexit process.

Fifty Labour MPs defied Jeremy Corbyn’s orders and backed single market membership in a vote on Thursday.

Three of them were subsequently sacked as frontbenchers.

The BBC understands the rebels think up to 90 Labour MPs back their cause and they could work with Tory MPs who also want a “soft Brexit” in future votes.

Prime Minister Theresa May and Labour leader Jeremy Corbyn both support leaving the EU’s internal market as a way of bringing to an end the free movement of EU citizens into the UK.

Labour’s manifesto called for the benefits of the single market and customs union to be retained after Brexit.

‘Key legislation’

But some MPs believe this is virtually indistinguishable from the government’s position, and want continued membership or access on equivalent terms, without which they say businesses will suffer and jobs will be lost.

Three shadow ministers – Ruth Cadbury, Catherine West and Andy Slaughter – were sacked by Mr Corbyn for defying his orders to abstain in a vote on an amendment to the Queen’s Speech, tabled by Labour’s Chuka Umunna, which pledged to remain in the single market and customs union.

Stephen Doughty, one of the 50 rebels, told the Guardian the fight was far from over.

“The key issue going forward is the extent to which Conservative MPs who have significant disquiet about the direction of Theresa May’s hard Brexit are willing to put their money where their mouth is and stand up for membership of the single market and customs union and other issues in key legislation coming forward.”

Another rebel MP told the BBC that there were up to 40 more colleagues who felt the same way but who had decided to sit on their hands in Thursday’s vote because it was “premature” and Tory MPs were unlikely to have backed a vote that might have toppled the government.

They would instead “take smaller steps – one thing at a time” and seek to co-ordinating their efforts with the Lib Dems, SNP and likely Tory rebels.

Parliament will be asked to approve eight Brexit-related bills over the next two years, framing new policies on trade, customs procedures and immigration.

‘Regrettable’

Another Labour MP, Wes Streeting, told Radio 4’s World at One he was “surprised and disappointed” at Jeremy Corbyn’s position, as he did not believe the party could “achieve its objectives of tariff-free, barrier-free access to the single market and a jobs first Brexit, outside of membership of the single market”.

There has also been a backlash against Mr Umunna in the wake of the vote, with some senior figures suggesting he had caused unnecessary division at a time when Labour is on a high.

“I just felt that given we’d come out of the general election with such an unexpected result, and there’s a real euphoria, to try and divide Labour MPs a week and a half in was a little disappointing,” deputy leader Tom Watson said.

And Stephen Kinnock, who like many Labour MPs did not take part in the vote, said the decision to fire the rebels was “regrettable” but “had to be done”.

Mr Umunna’s amendment was defeated by 322 votes to 101 as most Labour MPs did not take part.

A separate amendment proposed by shadow chancellor John McDonnell – which called for Brexit to deliver the “exact same benefits” as the EU single market and customs union – was defeated by 323 to 297.

The UK is due to leave the EU on 29 May 2019, although negotiations on the terms of exit have just begun.