London, March 24 (IANS): British Prime Minister Theresa May could gain support for her Brexit deal if she promises to stand down from her post, Conservative MPs told the BBC.

MPs in the ruling party said they might reluctantly back the agreement if they know she will not be in charge of the next stage of negotiations with the European Union.

If a third vote on May's deal does not take place this week and no alternative plan is put forward, the UK is set to leave the EU on April 12. And if the deal is passed, the bloc has agreed to extend the Brexit deadline until May 12.

The statement by the MPs comes as newspaper reports on Sunday claimed that cabinet ministers were planning to oust May and replace her with a "caretaker leader" until a proper leadership contest is held later in the year.

But Downing Street dismissed suggestions that May could be persuaded to stand aside, or that she would agree a "job share" arrangement where senior ministers would be given extra responsibilities.

Also on Saturday, hundreds of thousands of people marched in central London to call for another EU referendum.

Protesters carrying EU flags and placards called for any Brexit deal be put to another public vote, with speakers including Labour's deputy leader Tom Watson, Scotland's First Minister Nicola Sturgeon, and London Mayor Sadiq Khan.

Meanwhile, the woman behind a record-breaking anti-Brexit petition, retired lecturer Margaret Georgiadou, said she had received death threats over the poll.