A Lords amendment which sought to keep the UK in the EEA was rejected by the Commons on Wednesday by 327 votes to 126.
A total of 89 of Labour’s 257 MPs ignored front bench orders to abstain, with 74 voting in favour and 15 against.
They included six MPs who quit senior roles minutes before the vote in order to rebel.
Laura Smith stepped down as a junior shadow cabinet office minister to vote with the Government, saying “remaining in the EEA is not the right way forward for our country”.
Five parliamentary private secretaries voted in favour of the EEA amendment; Ged Killen, Ellie Reeves, Tonia Antoniazzi, Anna McMorrin and Rosie Duffield, with all but Ms Duffield announcing their resignation before the vote.
Just three Conservative MPs voted in favour of the Lords amendment, arch-Remainers Ken Clarke, Dominic Grieve and Anna Soubry.
The Lords amendment would force the Government to prioritise an EEA deal – the so-called Norway Model – in negotiations with the EU.
Corbyn under fire
Labour opposes the EEA model and had introduced its own amendment, 51A, which was defeated by 82 votes on Wednesday night.
Party leader Jeremy Corbyn said: “I understand the difficulties MPs representing constituencies which voted strongly for Leave or Remain have on the EEA amendment to the EU withdrawal bill.
“The Labour Party respects the outcome of the EU referendum and does not support the EEA or Norway model as it is not the right for option for Britain.”
The Conservatives said the resignations showed that Mr Corbyn “can’t lead his own party let alone our country through complex Brexit negotiations”.
Lib Dem leader Sir Vince Cable accused Labour of wasting an opportunity to defeat the Government, accusing Mr Corbyn of being “completely defunct as an Opposition Leader”.
He said: “Brexit is not inevitable, but we do need Labour’s front bench to do their job and join us in taking on the Tory government.”
Crewe and Nantwich MP Ms Smith said she resigned in order to vote with the Government against EEA membership, after Labour MPs were told to abstain.
She said on Twitter she could not vote for anything “that does not deliver the exit from the European Union that my constituents voted for”.
She added: “Remaining in the EEA is not the right way forward for our country. Taking rules from Brussels but having no role in making them is simply not good enough for Britain.”
In a letter to Mr Corbyn that he posted on Twitter, Mr Killen said he had to support “any measures that will allow the UK to maintain frictionless trade with the European Union”.
He wrote: “As such, while I will vote in favour of the Labour Party front bench amendment, I feel I must also support Lords Amendment 51, though I regret this will mean having to break the party whip and resign from my role as PPS, a decision I have not reached lightly.”
In her own letter, Ms Reeves added that she could not vote for any any measures she thought would be “detrimental” to those in her London seat of Lewisham West and Penge, which voted 2:1 in favour of Remain.
She added: “In recent weeks many hundreds of constituents have contacted me about their desire to remain in the EEA and my CLP (Constituency Labour Party) also passed a motion in May that was supportive of EEA membership.”
Trouble ahead for May
After days of division and bitter rows between Brexiteers and Remainers in the Tory ranks, Theresa May was able to see off another amendment that would have tied Britain to the customs union post-Brexit by 325 votes to 298, majority 27.
But the Prime Minister is likely to face the risk of further rebellions further down the line.
At Prime Minister’s Questions on Wednesday Mrs May said that Parliament cannot be allowed to “overturn the will of the British people” on Brexit.
She was speaking as she confirmed that the Government will table a new amendment to her flagship EU withdrawal bill, setting out in more detail the terms of the “meaningful vote” promised to MPs on the final Brexit deal.
Mrs May saw off a threatened defeat on the issue in the Commons on Tuesday by assuring would-be rebels personally that she would take their concerns on board.
But pro-EU Tories are warning that they remain ready to rebel if their demands are not satisfied by the compromise amendment, expected to be tabled on Thursday ahead of the bill’s return to the Lords on Monday.