London, Jan 19 : Theresa May needs to become a mediator to help break the Brexit deadlock in Parliament, former prime minister John Major has said.
He wants MPs to be given a vote on all Brexit options, indicating their preference on the way forward.
Mrs May should consider dropping her red lines "in the national interest" and become a facilitator to find out what Parliament wants, he said according to a BBC News report.
Tory Brexit supporter Suella Braverman dismissed his "Remainer elite" views.
She said: "Thank you Sir John, but no thanks."
No deal would be the "worst of all outcomes", Sir John warned. He said that "millions of people" - both individuals and businesses - would be hurt in such a scenario.
"Tinkering" with her deal will not make a difference to the current situation, he told BBC Radio 4's Today programme.
Mrs Braverman said some of the options being put forward - including a customs union, allowing continued free movement of people or holding another referendum - would be "clear breaches" of promises made by Mrs May, and ignore the will of the people.
She has also called for the Irish border backstop - the position of last resort, to maintain an open border on the island of Ireland - to be scrapped.
Sir John said the prime minister had been "handed a poisoned chalice" and that things had been "extremely difficult" for her.
"Her position has been all but impossible," he said, adding that Parliament was "running out of time".
If Mrs May does not drop her red lines "in the national interest", then her options are either for the Cabinet or Parliament to decide or for there to be another referendum "now more facts are known than were known in 2016", Sir John argued.
He said while Cabinet is too split to reach an agreement, there is hope that Parliament could reach a consensus, with Mrs May as a mediator.
He told the programme: "The prime minister argued valiantly for her deal. She fought for it but the House of Commons killed it and killed it comprehensively.
"The prime minister still needs a deal. If she can't deliver one that Parliament accepts, then she needs to become a facilitator, a mediator, to find out what Parliament will accept."
Ideally, all party leaders would give their MPs a free vote to allow an "honest representation" of opinion.
He called for compromise to prevent any further splits, as "no one is going to get their way".
It is now very unlikely we will leave the EU on 29 March "bar a miracle", he added, arguing that a delay would be "wise".
Meanwhile, shadow Brexit secretary Sir Keir Starmer is urging Parliament to take the "difficult decisions" necessary to end the deadlock over Brexit.
In a speech to the Fabian Society conference in London on Saturday, he will call for an "open and frank debate" to allow "credible solutions" to emerge.
He will say there are "no easy routes" out of the crisis.
It comes after Labour leader Jeremy Corbyn refused to meet Mrs May for talks to discuss a way forward unless she takes the possibility of a no-Brexit deal off the table. (UNI)