A vote in the House of Commons on Theresa May's alternative Brexit plan is scheduled to take place at the end of January.

The Prime Minister has until Monday to sketch out her intentions to MPs after the withdrawal agreement she struck with the EU was voted down by a huge margin on Tuesday.

She has entered into cross-party talks with opposition leaders to resolve the parliamentary impasse, meeting with SNP Westminster leader Ian Blackford on Wednesday night.

A follow-up to the meaningful vote, which May's government lost by 432 votes to 202, has been pencilled in for Tuesday, January 29.

The majority of 230 against the Prime Minister's deal was the biggest Commons defeat for a sitting UK Government in history.

With only 71 days until the March 29, when in law Britain will officially leave the European Union, May has urged MPs from all parties to serve the national interest and deliver on the 2016 Brexit result.

In an address outside Downing Street following cross-party talks, the Prime Minister said: "Now that we know what parliament doesn't want, we must all work constructively to set out what parliament does want."

But parties like the SNP, the Liberal Democrats and Plaid Cymru all support a second referendum - a so-called "People's Vote" - to give the British people the option to remain in the EU.

It is also backed by a significant number of Tory and Labour backbenchers, while a new YouGov poll shows a 12-point lead for staying in the EU if a fresh vote was held.

Speaking to STV News, the SNP's Ian Blackford said he told the Prime Minister in Wednesday night's meeting that she had "wasted the last two years" by not engaging with other parties sooner.

He continued: "I welcome the fact that we've had the offer of talks from the Prime Minister. That's the right thing to do and people throughout Scotland expect us to respond positively to that.

"We will engage in talks, but that's on the basis that everything is on the table, and in particular we need to have a discussion about extending Article 50.

"Let's remove the risk of the United Kingdom crashing out of the European Union at the end of March."

Blackford vowed to work "constructively" with May to find a solution, but said: "I will to say to the Prime Minister, if we can't, then she has to recognise that the people of Scotland have the right to make their own determination on where we go.

"And I'd simply make the point that in our view, independence for Scotland is going to be the best long-term solution for our interests."

He added: "Given the impasse, given the information we now know... we've got to have a discussion about a 'People's Vote', about putting it back to the people.

"If the Prime Minister is prepared to engage in such conversations then of course we would be delighted to do so as well.

"But it has to on the basis that these talks are real - it's not just window dressing - and there is an opportunity to move this on."

Labour has not yet thrown its weight behind such a move, with the party's current policy to win a general election and renegotiate a new withdrawal deal with Brussels.

However, the official opposition lost a no confidence vote against May's government on Wednesday by 19 votes.

The party's leader Jeremy Corbyn is refusing to enter into cross-party talks with the Conservatives until they rule out a no-deal Brexit.

Speaking at an event in Hastings, East Sussex, on Thursday, Corbyn blasted May's offer of talks as a "stunt".

In a direct message to her, he said: "Take no-deal off the table now please, Prime Minister."

But the Labour leader also suggested his party could back a second referendum if the UK Government "remains intransigent".

He continued: "If support for Labour's alternative is blocked for party advantage and the country is facing the potential disaster of no-deal, our duty will then be to look at other options which we set out in our confidence motion, including that of a public vote."

Corbyn added: "Last night's offer of talks with party leaders turned out to be simply a stunt, not the serious attempt to engage with the new reality that is needed."