Attempts to keep the UK in the European Economic Area after Brexit have been defeated in the House of Commons despite dozens of Labour MPs defying the leader's instructions on the issue.
MPs voted by 327 to 126 against a House of Lords proposal for a close relationship with the EU like Norway's.
Jeremy Corbyn urged his MPs to abstain but 75 voted for and 15 against, while six quit their Labour roles.
MPs overturned six further amendments peers had put forward.
What was the vote about?
MPs were deciding whether the UK should stay part of the European Economic Area after it leaves the EU - a similar arrangement to non-EU countries Norway, Iceland and Liechtenstein.
Like EU members, these countries are part of the EU single market - in return they are obliged to make a financial contribution and accept many EU laws. The free movement of people also applies in the zone as it does in the EU.
Supporters of the EEA argue it would give the UK the closest possible relationship with the EU without actually being a member, as it would offer full access to the single market.
But critics say it would require the UK to adhere to EU rules without having a say in them - and would not be in keeping with the spirit of the 2016 referendum result.
After the House of Lords altered the government's EU Withdrawal Bill in favour of EEA membership, the House of Commons agreed to change it back on Wednesday evening.
The government won the vote comfortably after Labour abstained, although three Tory MPs, Ken Clarke, Anna Soubry and Dominic Grieve, rebelled themselves and backed the motion.
Labour MPs were divided
Jeremy Corbyn said EEA membership was "not the right option" for Britain but that he understood the difficulties the issue posed for MPs representing strongly Leave or Remain constituencies.
Speaking on BBC Radio 4's Today programme, Labour MP Laura Smith defended her decision to quit as shadow defence minister because she did not want to follow the leader's instruction to abstain.
The MP for Crewe and Nantwich said she wanted to oppose the Lords amendment, saying remaining part of the EEA was not in the interests of her constituents who had voted to leave the EU in 2016.
Ms Smith, who backed Remain in the referendum, said there were "legitimate reasons" why people had backed Brexit, adding: "The country is divided on this issue and we need to start bringing people together."
On the other side of the debate were her Labour colleagues Ged Killen, Tonia Antoniazzi, Anna McMorrin, Ellie Reeves and Rosie Duffield who stepped down as parliamentary private secretaries to support EEA membership.
In her resignation letter to Mr Corbyn, Ms Reeves said her Lewisham West and Penge constituency had voted by two to one to stay in the EU and hundreds had contacted her in support of staying part of the EEA.
Earlier, Labour failed in an attempt to amend the bill with their own alternative motion to guarantee "full access" to European markets after Brexit from outside the EEA. This was defeated by 322 votes to 240..
Westminster sausage machine
By political editor Laura Kuenssberg
A wiser head than me - there's dispute over whether it was Mark Twain or Bismarck! - once remarked that laws are like sausages, if you respect them it's best not to watch them being made.
Well the last 48 hours in Westminster may give weight to that. Farce? Fiasco? Or maybe today in Parliament has been in the best tradition of British pantomime.
Or perhaps, this is in fact the completely predictable agony of split political parties, with leaders who struggle to command their troops, just trying to make it through after a huge vote that by its very nature, split the country in two.
Why were MPs voting about Brexit?
The government is trying to pass a new law, called the EU Withdrawal Bill, which it says is needed to ensure a "smooth and orderly Brexit".
Its main purposes are to end the supremacy of EU law in the UK, and transfer existing EU law into UK law so the same rules and regulations apply on the day after Brexit.
But as it passes through Parliament, MPs and peers have been trying to change it, in some cases adding bits on that would change the government's Brexit strategy.
MPs also overturned other changes made to the bill by the Lords, including a requirement for ministers to set out steps to negotiate a customs union with the EU.
The government agreed a compromise with potential Tory rebels earlier this week to work towards a "customs arrangement" with the EU. This won the support of the Commons by 325 votes to 298.
Other changes insisted upon by the Lords relating to the Charter of Fundamental Rights, principles of EU law to be retained after Brexit and EU environmental principles were also removed.
In response to the votes, Lib Dem leader Sir Vince Cable accused Labour of conspiring with the Conservatives to "wave through a hard Brexit".
But ministers did make one significant policy concession - on refugee policy after Brexit.
They accepted a proposal by Labour MP Yvette Cooper to widen the terms under which unaccompanied child refugees can be reunited with family members living in the UK.
The government had already agreed to allow unaccompanied children to claim asylum in the UK if it was deemed to be in their "best interests".
But, following Ms Cooper's intervention, ministers have agreed to drop a clause stating this could only happen if their family members already in the UK were over 18 years of age.
Solicitor General Robert Buckland said ministers had listened "very carefully" to the views of MPs from different parties and would amend the bill when it returns to the Lords next week.