BBC Brussels reporter Adam Fleming says EU leaders are considering making a commitment to continue negotiating a trade deal with the UK even if the Irish backstop comes into force.

He says the move is aimed to reassure the House of Commons that the backstop will be a temporary measure.

However he notes that this would not be a legally binding commitment.

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Conservative MP Stephen Crabb said that the prime minister still faces a huge challenge in winning over those MPs who voted against her.

Speaking outside Parliament, he said: "Those MPs who voted against her today, a lot of them will also be voting against her in terms of the substance of the Brexit deal. So it is hugely challenging.

"It seems there isn't a majority in the House of Commons at the moment for any solution to Brexit - not for a second referendum, not for a Norway-style deal, not for her deal.

"But Parliament has to say yes to something - and she has been given a new mandate to get on and find that something."

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5 Live has been hearing from callers – who have had a mixed reaction to Theresa May’s win.

Jan from Thetford, who voted remain, said she supported the prime minster and her deal.

“I’m pleased that she won. I think she’s come up with the best we can have – and I hope somehow she can get it through. It’s not perfect, nobody’s happy with it. But it’s less bad than anything else there is.”

Caller Richard was less happy with the result: “I would’ve liked to have seen a new leader,” he said.

“We are now in a stage where she’s obviously won the confidence vote, but the bright side is that no deal is more likely than her deal.”

Mahvash in Leighton Buzzard said May “deserved to win the vote”.

“She’s been in a position that she didn’t ask for. She’s done her best and put up with a lot from her backbenchers; her ministers resigned because they didn’t agree – they were more thinking about their own political situation, not the country.”

Caller Harris is originally from Germany, but now lives in Brighton. He said the prime minister did not get enough votes to "convince the public that she has the support " of her own party.

"We’re back at the beginning - Theresa May has no majority for her deal and she’s now trying to find a solution, but I’m not expecting her to find one”.Click here to listen.

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MP Simon Hoare disagreed with Jacob Rees-Mogg that Theresa May should resign.

And he said of his colleague: "Losing with bad grace and churlishness and just being a bad sport is not what people expect.

"He’s orchestrated this with some of his colleagues, he’s got the ballot, we’ve had it, we’ve got the result.

"Let’s now stop moaning and picking away at things, lets come back heal, unite and deliver."

"This has been a long and challenging day, but at the end of it I'm pleased to have received the backing of my colleagues in tonight's ballot.

"Whilst I am grateful for that support, a significant number of colleagues did cast a vote against me, and I have listened to what they said.

"Following this ballot we now need to get on with the job of delivering Brexit for the British people and building a better future for this country.

"A Brexit that delivers on the votes that people gave, that brings back control of our money, our borders and our laws.

"That protects jobs, security and the union, that brings the country back together rather than entrenching division.

"That must start here in Westminster with politicians on all sides coming together and acting in the national interest.

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"For my part I have heard what the House of Commons said about the Northern Ireland backstop and, when I get to the European Council tomorrow, I will be seeking legal and political assurances that will assuage the concerns that members of Parliament have on that issue.

"But while delivering Brexit is important we also need to focus on the other issues that people feel are vital to them and matter to them today.

"The issues that we came into politics to deal with, building a stronger economy, delivering first-class public services, building the homes that families need.

"We owe it to the people who put us here to put their priorities first.

"So here is our renewed mission: delivering the Brexit that people voted for, bringing the country back together, and building a country that truly works for everyone."

The Tory party chairman has hailed the vote for Theresa May and compared it to a previous result.

Brandon Lewis said: "She’s got over 63% of the vote, that’s a phenomenally high figure and more than than she got when she won the leadership vote in 2016."

Scottish Secretary David Mundell has welcomed the prime minister's victory, saying she had won "convincingly" and it was now time to "get on with delivering an orderly exit from the EU".

Eleven of the 13 Scottish Conservative MPs said they would be voting for Mrs May ahead of the secret ballot.

Scottish Tory leader Ruth Davidson also gave Mrs May her "full support".

Read more on Scottish Tories reaction here.