Theresa May was battling to convince lawmakers within her Conservative Party to back her Brexit withdrawal deal on Sunday amid reports that senior ministers in her Cabinet were planning to force her resignation.
Mr Bryant added: "It's not Parliament that can decide whether we stop Brexit or not, the only people who can do that is the British public".
In a stinging attack on the cabinet conspirators, he called for the Prime Minister to sack those involved, who he said were "not fit for their positions".
Article 50 of the Treaty of the European Union lays out the procedure for member states to voluntarily leave the EU. "This is now the moment of maximum opportunity - we need to avoid the catastrophe of no-deal and the damage which would be caused by the prime minister's bad deal".
The paper reports that her de facto deputy and close ally David Lidington is being lined up to take over, while The Mail on Sunday says Environment Secretary Michael Gove is the "consensus choice" for the job.
The British people didn't vote for a bad Brexit deal.
The prime minister has found her authority weakened after a series of setbacks in Parliament and her inability to win meaningful concessions from European Union leaders who refuse to sweeten the Brexit deal.
A week prior to Saturday's People's Vote march, a pro-Brexit group began a projected two-week march of their own from Sunderland to London.
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Following a request by Prime Minister Theresa May, the European Council agreed on Thursday, March 21 to extend the UK's departure date to 22 May 2019, provided the Withdrawal Agreement is approved by the House of Commons by March 29, 2019 at the latest.
Speculation was heightened further when George Freeman, a Conservative MP and former policy adviser to May, said on Saturday evening that it was "all over" for May. "Well, have a look out of the window, prime minister".
With Britain mired in political paralysis over Brexit hundreds of thousands of pro-Europeans thronged London on Saturday calling for another referendum on European Union membership, in one of the biggest protests in decades. Everyone feels betrayed. Government's gridlocked.
Nadhim Zahawi said Parliament would have "failed" if the twice-defeated Withdrawal Agreement is rejected by MPs again, as he said he was "not prepared" to tell his constituents the United Kingdom would not leave the European Union. Parliament has already voted the agreement down twice. "What we expect to see is more waiting time for goods and people when crossing the border into the continent". "Carrying placards and flags, and with blue wigs, face paints and other fancy dress, the crowd chanted slogans in English and Spanish, such as "¡Derechos sí, Brexit no!
Watson, the Labour Party's deputy leader, also spoke in support of another referendum, saying it would bring the country back together.
One million people, organizers claimed, marched through London demanding a second referendum on Saturday, and 5 million have signed an online petition urging the government to revoke Article 50 and cancel the Brexit process altogether. The deal was defeated in parliament by 149 votes on March 12 and by 230 votes on January 15.
According to Buzzfeed, the prime minister was told to think about leaving office by several of her whips during a meeting, but Mrs May was "unmoved", refusing to believe it would make any difference to the deal.