Image source, EPA/WILL OLIVER

"Theresa May appears to have marched her depleted troops to the top of the hill only to lose her nerve," says Lib Dem leader Sir Vince Cable.

"She is hopelessly weakened. There is little point postponing the vote when nothing concerning the deal will change.

"The Conservatives are wilfully prolonging Brexit uncertainty because they can't get their deal through Parliament.

"This deadlock must be broken by giving the people the final say, including the opportunity to remain in the EU."

Tory Brexiteer Nigel Evans says the PM has made a "very wise decision" to delay the vote.

He told BBC News that it shows she is "listening", adding: "I'm not going to criticise my prime minister for listening."

He said the PM now has "very strong authority from Parliament" to go back to Brussels and renegotiate.

"It buys the PM a little bit of time, not to save her skin, but to ensure she completes that contract with the British people - goes back to Brussels and says we’re not separating Northern Ireland from the UK and we'll have to leave unilaterally - you have to give me this - otherwise I'm not going to push that to Parliament.”

"Deferring the vote is only of any use if the government is prepared to go to Brussels and insist on necessary changes to the withdrawal agreement," Democratic Unionist Party deputy leader Nigel Dodds said.

"Few people accepted this was the best deal available and the prime minister's actions today prove that."

Theresa May relies on support from the DUP to keep her government in power.

Northern Ireland parties Sinn Féin, SDLP, Alliance and NI Greens have released a joint statement reiterating their preference for "no Brexit at all".

"We have a shared responsibility to protect jobs, economic stability, the environment and people's livelihoods," the statement reads.

"At the very least, this means avoiding a hard border, protecting the Good Friday Agreement and hard won peace of the past 20 years, and staying within the Single Market and a Customs Union.

"Therefore as a basis for this, we maintain that there is a pressing need for the backstop as set out in the Withdrawal Agreement to be banked.

"By contrast, we believe that a no deal situation would be catastrophic for our economy and society."

Image source, Michelle Devane/PA Wire

Irish PM Leo Varadkar says it is not possible to renegotiate the Irish border backstop proposal without "opening up all aspects" of the Brexit withdrawal agreement.

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At least five Conservative MPs are saying on Twitter that they are not happy about the Brexit withdrawal agreement vote being delayed, and they will vote against such a delay.

Some government sources are insisting there doesn't need to be a vote from ministers in order for the PM to delay the vote in Parliament - but there is still a lot of confusion about this.

Plaid Cymru's Westminster leader Liz Saville Roberts said: "The prime minister is running scared. She can only delay the inevitable loss.

"She made promises that she cannot deliver and now she is coming up against reality.

"The only single person who can stop a no-deal Brexit is the prime minister. By delaying this vote she is personally making a no-deal Brexit more likely.

"The prime minister wants to deny the public a say in a People's Vote and now she is trying to deny MPs a vote too. She is denying democracy on all fronts.

"People deserve better than the chaos in Westminster. Now we know the truth about Brexit, people must be given the right to decide whether the reality of leaving the European Union is what they want."

The BBC's deputy political editor Norman Smith says:

"Many Tory MPs and ministers will be drawing a huge sigh of relief because the parliamentary arithmetic looked inescapable.

"Mrs May was heading for a catastrophic defeat.

"If she doesn't manage to get some sort of concession on the backstop the parliamentary arithmetic will still be staring her in the face."

Many critics of the withdrawal agreement chiefly objected to the existence of the Northern Ireland backstop in the deal.

The backstop is a position of last resort, to maintain an open border on the island of Ireland in the event that the UK leaves the EU without securing an all-encompassing deal.

Both the UK and the EU have said they want to avoid the return of a "hard border" after Brexit.

Last week the Attorney General Geoffrey Cox said the way the agreement was drawn up meant the UK could be "indefinitely committed" to the EU customs rules if Brexit talks broke down.

The Reuters news agency is reporting that a junior minister has said the PM will head back to Brussels to discuss Brexit.