The prime minister insisted she would not resign after European leaders agreed to delay Brexit until 31 October in late-night talks in Brussels.
The second delay to the Brexit process - initially intended to conclude on 29 March - averted a no-deal withdrawal on Friday with less than 48 hours to go.
However, it infuriated anti-EU Conservative MPs, who insisted the UK should have instead left the EU without a deal.
As she updated MPs in the Commons, Ms May faced calls from veteran Tory Sir Bill Cash to step down. He accused her of an “abject surrender” and asked if she would resign. Ms May replied: “I think you know the answer to that”.
Another Brexiteer, Peter Bone, asked the prime minister if she planned to “honour” her vow not to delay Brexit beyond 30 June.
But the prime minister insisted she could still get a Brexit deal through parliament and said cross-party talks with Labour must “press on at pace”.
It came after a marathon European Council meeting to discuss the UK's request to delay Brexit until 30 June. Most EU leaders had wanted a much longer extension but settled on the date of 31 October after strong opposition to a lengthy delay from French president Emmanuel Macron.
Afterwards, Council president Donald Tusk admitted it was his “quiet dream” that the UK would remain in the EU.
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Ms May, who will deliver a statement in the Commons on Thursday, told MPs weeks ago that she was “not prepared to delay Brexit any further than 30 June” as prime minister and would resign once this stage of talks was complete.
Good morning and welcome to The Independent's live coverage as Theresa May prepares to address MPs after agreed a six-month delay to Brexit.
The prime minister is likely to face anger from Conservative backbenchers in the Commons after European leaders agreed to extend the UK's membership of the EU until 31 October.
In a press conference in the early hours of Thursday, European Council president Donald Tusk did not rule out further extensions beyond October.
And he sent a message to the UK: "This extension is as flexible as I expected, and a little bit shorter than I expected, but it's still enough to find the best possible solution.
"Please do not waste this time."
Theresa May is set to enrage her critics within the Conservative party after setting herself up to stay on as prime minister until the winter while presiding over a long delay to Brexit, writes our Europe correspondent Jon Stone. Here's the full story:
Jeremy Hunt, speaking on Robert Peston's ITV programme last night, has admitted the Brexit deal could be changed by a future prime minister:
Brexit minister Kwasi Kwarteng has insisted that delaying Brexit until October will give the government time to get an exit deal through parliament.
He told BBC Radio 4's Today:
"It is not a secret that we have had a difficult time in trying to get the deal through the House of Commons.
"Parliament is in gridlock at the moment and I think that we have got the time, hopefully, to get the deal through.
"But it's been challenging.
"I think that the extension is long enough to get a deal through."
Last night Theresa May and EU leaders agreed to delay Brexit until 31 October - a longer extension than the prime minister wanted, but shorter than many in the EU were pushing for. Here's our full report on the night's events:
The action in the House of Commons gets underway at 9.30 this morning. Here's today's order paper:
John Bercow has granted one Urgent Question in the Commons today, which will see Labour's Clive Betts ask the Department for Transport about Stagecoach.
There is also a government oral statement on discrimination in football, meaning Theresa May's statement on Brexit will be pushed back until around 1pm.
Donald Tusk, the president of the European Council, has admitted it is his "quiet dream" that the UK stays in the EU
Theresa May will update MPs this afternoon on the outcome of last night's European Council meeting. When she rises in the Commons around 1.00pm, we expect the prime minister to deliver a statement similar in content to the one she gave to the media in Brussels in the early hours of this morning.
She will likely insist that her main priority was ensuring that the UK can exit any extension early if it ratifies the withdrawal agreement, which the EU agreed to, and re-iterate that she does not want Britain to take part in European Parliament elections on 22 May.
The prime minister will once again stress the need for MPs to work together to find an exit deal that parliament can agree to. She will likely say that talks with Labour are continuing and that the public wants a resolution to be reached. Expect a few jibes at parliament for voting down her deal three times, along with a lot of comments about how disappointed she is that Britain is still in the EU.
Will it change anything? Don't count on it.
This is an interesting development. Scottish secretary David Mundell has said the government is "willing to discuss" the possibility of a customs union with the EU - a key demand of Labour and one of the main barriers to cross-party talks progression.
He told BBC Radio Scotland:
"The government is certainly willing to discuss a customs union, but a customs union would require to command a majority of support in Parliament.
"A customs union has been put forward previously in parliament and hasn't commanded a majority, partly because we've had the usually politicking, the SNP who say they support a customs union then didn't vote for it.
"So nothing that goes forward will actually be successful unless we can command majority support for it in parliament."
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