Britain will be in "uncharted waters" if lawmakers do not approve the Brexit deal Theresa May has negotiated with Brussels, the prime minister warned in an interview published Sunday.

"When I say if this deal does not pass we would truly be in uncharted waters, I hope people understand this is what I genuinely believe and fear could happen," she told the Daily Mail.

"It would mean grave uncertainty for the nation with a very real risk of no Brexit or leaving the European Union with no deal."

May is facing a revolt from lawmakers within her own Conservative party, and it appears unlikely she will gain the votes to pass her deal when parliament votes on it Tuesday.

But Downing Street late Saturday rejected reports that May could delay the vote to avoid defeat, with a spokesman saying: "The vote is going ahead on Tuesday."

The Times newspaper had reported that ministers and aides had convinced May to delay the vote and travel to Brussels to demand a better Brexit deal, saying she needed a "handbag" moment with EU leaders.

The phrase dates back to prime minister Margaret Thatcher reportedly throwing down her handbag at a summit with EU leaders in 1984 and declaring "I want my money back." She won a rebate for Britain from the EU budget.

Meanwhile, another lawmaker resigned from his role as ministerial aide to Defence Secretary Gavin Williamson over May's deal, blaming the backstop plan to maintain an open Irish border.

Writing in the Sunday Telegraph, Will Quince said the plan could leave Britain "tied to the negotiating table for years, until we agree to anything in desperation."

"I do not want to be explaining to my constituents why Brexit is still not over and we are still obeying EU rules in the early 2020s or beyond," he wrote.

The paper reported that another parliamentary private secretary was on the verge of quitting and that Penny Mordaunt, secretary of state for international development, could also resign.

May has suffered a string of resignations from ministers in recent months, including former foreign secretary Boris Johnson and former Brexit secretaries David Davis and Dominic Raab.

Pro-Brexit activists are set to hold a march in London on Sunday, while counter demonstrators will hold a rival protest.

Meanwhile, a separate rally will also be held in London calling for a second referendum on Brexit, organized by the pro-EU Best for Britain campaign and the People's Vote organization.