May has until the end of next week to get a deal through Britain's Parliament.
Proposed by opposition Labour lawmaker Yvette Cooper and supported by more than 30 lawmakers, including Conservatives, it calls on the government to set out by the end of March 28 - if parliament has not approved May's deal by then - how it will ensure Britain does not leave the European Union on April 12 without a deal.
May has repeatedly dismissed calls for a second referendum despite parliament so far failing to agree on a deal for Britain to exit the European Union.More news: Ronald Koeman says Netherlands deserved point against Germany
There are two dates set for Brexit based on how MPs vote in the third meaningful vote on the Prime Minister's deal.
The organisers of Saturday's march described it as one of the biggest protest marches in British history, and said it had far exceeded expectations. At the endpoint of the march outside parliament, speakers including Scotland's First Minister Nicola Sturgeon, London Mayor Sadiq Khan and opposition Labour deputy leader Tom Watson rallied the crowds through the afternoon.
Numerous protesters ended up at Parliament Square, where speakers took the stage in the rally to encourage participants, the Guardian reported.
The longer delay would allow time for a change in prime minister if the growing list of May's opponents in the Conservative Party manage to force her out.More news: Motorola One Vision press render surfaces online
Labour MP Chris Bryant told talkRADIO Theresa May was wrong to suggest MPs sought to overturn "the will of the people" in her Downing Street statement last week.
Conservative Dominic Grieve said: "The vote last week was not a serious vote, it was always apparent when it was moved that there were large numbers of MPs who might support it who didn't think it was the right moment to take place, so I don't think one should make a judgement on its viability like that". "The way to reunite our country is to decide on our future together". "Let the people take control".
Meanwhile, a petition calling for the whole Brexit process to be scrapped shot past the 4-mn mark. "We are now a Remain country. A People's Vote may not happen - so vote now". According to the relevant laws and regulations of the United Kingdom, once a petition exceeds 10,000 signatures the government must respond publicly and if the number of signatories surpasses 100,000 then parliament must conduct an open debate on the matter.
But not everyone is convinced that those who voted in the original referendum have changed their minds.More news: Salman Khan, Ram Charan, Samantha at wedding of Venkatesh's daughter in Jaipur
Elsewhere, former Ukip leader Nigel Farage hit out at the London march as he claimed "we are the majority" at a pro-Brexit rally in Nottinghamshire.
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