A Downing Street source said: "The Prime Minister was clear at the start of cross-party talks that there are principles underpinning these talks".
As things stand now, Britain is scheduled to leave the European Union bloc on March 29 without an agreed upon withdrawal plan.
With much of the focus now on Labour, its Brexit spokesman Keir Starmer said there was now only really two options that could find majority support - a future close economic relationship with the European Union or a second referendum - and that it was increasingly inevitable that Article 50 would be extended.
The future of the Brexit agreement is now unclear and a no-deal scenario, which implies a United Kingdom withdrawal from the European Union without formal arrangements for the post-Brexit relationship between the two sides, remains highly possible.
Such a vote could trigger a general election but this is very much the nuclear option for Tory rebels and the DUP have already said they will not vote with Labour, so it appears to be a forlorn hope.
Mr Blackford said: "With the clock ticking it is concerning that there has been little indication so far that the Prime Minister understands the implications of the defeat she suffered last week and the steps that now need to be taken". The talks have produced few signs that May plans to make radical changes.
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Britain's Labour Party is calling for an "open and frank debate" on the government's stalled Brexit plan and an increased role for Parliament - but still won't meet with Prime Minister Theresa May for talks.
That left Britain facing the prospect of no deal to smooth its exit from the European Union in little more than two months' time.
The amendment would also kill May's Brexit deal.
Jeremy Corbyn's unwillingness to back a second referendum could lead to a near-fatal split in the Labour Party, David Lammy has warned.
According to the New Statesman, the vote could come as soon as February 28.
The EU has repeatedly said changes can not be made to the legally binding withdrawal agreement struck by Theresa May and EU leaders and which contains the terms of the backstop.
"Parliament has not got the right to hijack the Brexit process because parliament said to the people of this country: "we make a contract with you, you will make the decision and we will honour it", Fox said.