Tory rebels reject May's Brexit PlanB | Ireland
The move would give Parliament control over the Brexit process if Mrs May fails to secure a deal by February 26.
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Ireland said the backstop was staying and the European Commission repeated on Monday that the withdrawal agreement text, and its backstop component, is not open for renegotiation.
International Trade Secretary Liam Fox, however, insisted that backing the amendment would strengthen the Prime Minister's hand when it came to reopening negotiations on the backstop - meant to ensure there is no return of a hard border on the island of Ireland.
This calls for MPs to be able to vote on options to stop a no-deal exit, such as a customs union with the EU, as well as the possibility of a new Brexit referendum.
However, he suggested that he could be prepared to support it if the amendment had official Government backing.
The backstop is a type of insurance policy aimed at preventing a hard border between the Republic of Ireland and the British province of Northern Ireland if no other solutions can be agreed.
The question is in two weeks time will there be an irrevocable undertaking that her deal will be brought back, amendable by exactly the kind of amendments there are today to rule out no Brexit, or, if a deal is not brought back, there is the same platform?
The BBC's Laura Kuenssberg says Labour believes the amendment would "give MPs a temporary window to agree a deal" that could unite the country.
One amendment could see Article 50 extended if no agreement is reached by February.
In a statement this morning, DUP leader Arlene Foster said she believes the plan can unify a number of strands in the Brexit debate and urged the Prime Minister to get behind it.
The crux of the deal is an extension to the current transition period - possibly to December 2021 - to give the United Kingdom more time to negotiate a free trade deal with the bloc.
The plan is said to have been relatively warmly received by Conservative MPs across the Brexit divide.
Prime Minister Theresa May arriving in Downing Street.
"What a cunning plan", one European Union official is said to have remarked sarcastically, while an European Union diplomat was reported to have said, "This is just nonsense", according to The Guardian.
Arch EU sceptic Jacob Rees-Mogg is working with Steve Baker and Iain Duncan Smith, as well as Remainers Nicky Morgan and Stephen Hammond on the scheme, the Guardian reports.
"We have seen the German economy weakening, we have seen the French economy weakening", he told BBC Radio 4's Today programme.
They pointed out that the new proposal does nothing to prevent a hard border in Ireland - which the backstop arrangement is meant to address.
Dr Fox said that MPs' backing for the Brady amendment would strengthen the Prime Minister's hand.
Amendments that could alter the path of Brexit altogether are what really matter.
However, the Opposition will seek to limit the delay to the UK's departure from the bloc.
She hopes that if she succeeds it will give her a mandate to wring concessions from Brussels over the most controversial element of the divorce deal. Jeremy Corbyn has been careful not to commit Labour to officially back such a poll, though.
What's the problem with the Irish backstop?
May's so-called Irish backstop was the reason why, with the arrangement causing widespread dismay across all parties.
Brexiters fear being stuck in a customs union would kill off their hopes of the United Kingdom furthering an independent trade policy.
She said that the Malthouse plan - to redraft the "backstop" and possibly leave the European Union without an agreement - was "a serious proposal that we are engaging with sincerely and positively".