The vote came after Prime Minister Theresa May’s Withdrawal Agreement was rejected for the second time on Tuesday, and MPs voted the following day to rule out a no-deal Brexit.
A motion in May’s name, authorising her request for an extension to the two-year Article 50 negotiation process, was passed by 412 votes to 202 – a majority of 210.
Only a refusal by the leaders of the 27 remaining EU states to grant the UK an extension at a Brussels summit next week could now preserve the totemic date of March 29 as Brexit Day.
May has made clear that she will press her Agreement to a third “meaningful vote” in the Commons by March 20, in the hope of securing the support of MPs who rejected it by 230 votes in January and 149 earlier this week.
If she succeeds, she will go to Brussels next Thursday to request a short delay to a date no later than June 30, to give herself time to get her deal through the UK parliament.
But if her deal is rejected for a third time, she believes any extension would have to be far longer and would involve the UK taking part in European Parliament elections in May.
Earlier, MPs decisively rejected an attempt by the Independent Group to secure a second referendum on Brexit by 334 votes to 85.
And by the far narrower margin of 314-312, they voted down a cross-party bid for Parliament to seize control of the Brexit process by forcing a set of “indicative votes” to determine the preferred Brexit outcome of the House of Commons.
A Labour Party amendment demanding an extension to Article 50 withdrawal negotiations to provide time to “find a majority for a different approach” was also defeated.
Labour whipped its MPs to abstain on the referendum vote, but 24 voted in favour – not including Brighton’s Lloyd Russell-Moyle, who went through both lobbies to cancel his own vote out.
Labour revealed that leader Jeremy Corbyn and senior aides have met with backbenchers Peter Kyle and Phil Wilson, who are promoting a plan to accept Mrs May’s deal on the condition that it is subject to a second referendum.
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