Media playback is unsupported on your device Media caption Theresa May: “What we are looking for is a deal that is right for the United Kingdom"

An agreement to move on to the next phase of Brexit talks is "good news" for both Leave and Remain voters, Theresa May has told MPs.

She told Parliament it should reassure those who feared the UK would get "bogged down" in endless negotiations or "crash out" without a deal.

She said the UK did not want a trade arrangement based on any other country but "a deal that is right for the UK".

Labour leader Jeremy Corbyn said Mrs May had only just "scraped through".

The negotiations so far, he said, had been "punctuated by posturing and delays", with confusion about how legally watertight the agreements were.

Updating Parliament on the terms of Friday's phase one agreement - which is expected to be approved by the other 27 EU leaders later this week - the PM said it would see the UK pay a "fair" divorce bill, avoid a hard border between Northern Ireland and the Republic of Ireland and see the rights of UK and EU expat citizens "enshrined in UK law and enforced by British courts".

But she said that if the UK was not able to agree a withdrawal deal with the EU prior to its scheduled exit in March 2019, "this deal is off the table".

Earlier, the EU said that although the agreement was not strictly legally binding, the two sides had "shaken hands" on it with a "gentleman's agreement" between David Davis and Michel Barnier.

On Sunday the Brexit Secretary David Davis said guarantees on the Northern Ireland border were not legally binding unless the two sides reached a final deal.

But he told LBC Radio on Monday they would be honoured whatever happened.

The BBC's assistant political editor Norman Smith said the Brexit Secretary's clarification - in which he insisted one of the government's key aims was to ensure that the Northern Ireland peace process was not harmed - came after concerns in Dublin about the enforceability of Friday's phase one agreement.

Media playback is unsupported on your device Media caption David Davis: "No deal means we won't be paying the money"

Mr Davis said he had been taken out of context when he appeared to tell the BBC's Andrew Marr that guarantees designed to avoid a hard border on the island of Ireland were a "statement of intent".

"What I actually said yesterday in terms was, we want to protect the peace process, want to protect Ireland from the impact of Brexit for them," he said.

"I said this was a statement of intent which was much more than just legally enforceable. Of course it's legally enforceable under the withdrawal agreement but even if that didn't happen for some reason, if something went wrong, we would still be seeking to provide a frictionless invisible border with Ireland."

A European Commission spokesman said the first-phase deal on the Northern Ireland border, the divorce bill and citizens' rights did not strictly have the force of law.

"But we see the joint report of Michel Barnier and David Davis as a deal between gentlemen and it is the clear understanding that it is fully backed and endorsed by the UK government."

Media playback is unsupported on your device Media caption Citizens' rights, the Irish border and money are the three big negotiation points

She added: "President Juncker had a meeting with Prime Minister May last Friday morning to ascertain that this is precisely the case. They shook hands."

In her statement to Parliament, Theresa May said she expected EU leaders to agree immediately to start talks about a two-year transition deal immediately, paving the way for continued access to the single market for a time-limited period.

"This is good news for the people who voted Leave, who were worried that we were so bogged down in the negotiations, tortuous negotiations it was never going to happen," she said.

"It is good news for people who voted Remain, who were worried we were going to crash out without a deal. We are going to leave but we are going to do so in a smooth and orderly way."

'Christmas present'

The prime minister, who also written an open letter to EU nationals in the UK, was praised by leading figures from both wings of the Tory party.

On the pro-EU side, Anna Soubry said there was "complete unanimity" within the party that Friday's agreement was a "major step forward" while Nicky Morgan said it was an "early Christmas present".

While commending the PM, former Conservative leader Iain Duncan Smith, who had urged her to walk away from the talks if there was no progress, sought reassurances the transition period would be used to "implement things that have been achieved" and "not carry on with no change".

In response, the PM said firms needed time to adjust and avoid the danger of a "double cliff-edge" change in rules - but she also said there would be changes such as EU citizens arriving in the UK having to register.

For Labour, Mr Corbyn said the government's "shambolic" approach was continuing with ministers "contradicting themselves" over whether the UK would pay a financial settlement if there was no trade deal.

Lib Dem leader Sir Vince Cable told BBC Radio 4's Today programme on Monday that the EU was unlikely to offer the UK a bespoke trade deal modelled on the one it has with Canada, but with financial services included.

"The EU has effectively ruled that option out," he said. "The EU has also said if you want a Canadian-style approach you have to link it to all kind of conditions to do with state aid, environmental rules and employment rights which effectively rules out the government's philosophy of taking back control".

His party has tabled an amendment to the EU Withdrawal Bill - to be considered on Tuesday - which would see "the Norway option" of remaining in the single market kept open as long as possible.

Urging Labour MPs and "pragmatic" Tories to support this approach, he said it was "inferior to where we are but it is better than the alternative of not having a close relationship with the EU".