British MPs will on Wednesday hold votes on various Brexit options even as Prime Minister Theresa May comes under pressure to announce a departure plan to get support for her unpopular divorce deal.

Three years after a referendum in which Britain voted to leave the European Union, the country is gripped by painful uncertainty over how -- or even whether -- it should put an end to its 46-year membership.

May's deal negotiated with Brussels has already been voted down overwhelmingly by parliament twice but the government is widely expected to present it for a third time on Thursday to ensure an orderly Brexit.

EU leaders said Britain could leave the EU on May 22 if the deal is adopted this week, or face a potential no-deal Brexit as early as April 12. In a bid to find Brexit alternatives, lawmakers took the unprecedented step on Monday of seizing control of Wednesday's parliamentary business.

MPs will hold a series of "indicative votes" -- indicating their preferences on a piece of paper -- for different Brexit outcomes, although May is not legally bound to follow their instructions.

The proposals put forward to include a customs union with the EU, remaining in the single market, holding a second referendum or stopping Brexit by revoking Article 50 -- the formal notification for departure.

The alternatives that will actually be voted on will be selected by Speaker John Bercow on Wednesday and voting will take place at around 1900 GMT with the results expected at around 2100 GMT.

Time has been set aside next Monday to try and whittle down the most popular options to a final plan.

Parliament's unprecedented power-grab was spearheaded by arch-EU MPs, who want to either reverse Brexit or preserve much closer economic ties with the remaining 27 states.

Three members of May's government quit in order to vote for the move, further piling pressure on their leader.

However, she received a boost on Tuesday when influential Brexiteer Jacob Rees Mogg suggested he could back her deal in order to make sure the whole process was not stopped.

Prominent Brexit supporter Boris Johnson has already indicated that he could back the deal, but only if May agrees to go, raising suggestions that she could announce plans for her departure at a meeting with Conservative MPs at 1700 GMT on Wednesday.

"If the Prime Minister announces a timetable of departure, I think that's going to swing a lot of people behind her deal, we could get it over the line," said Conservative MP Nigel Evans.

But the Democratic Unionist Party (DUP), the hardline Northern Irish power brokers who prop up the government, have poured cold water on the deal.

The group's Brexit spokesman Sammy Wilson said the party would rather see a one-year Brexit delay.

"Even if we are forced into a one-year extension, we at least would have a say on the things which affect us during that time and would have the right to unilaterally decide to leave at the end of that one-year," he wrote in the Daily Telegraph.

"We won't let the PM or the Remainer horde in parliament bully us into backing a toxic Brexit," he said.

Britain was originally due to exit from the EU on March 29, and MPs will vote on Wednesday to formalise the extension into law.

It has already been written into international law and is expected to pass easily, with May's office saying that "there would be uncertainty for citizens and businesses" if MPs were to reject it.

A group of Brexit-supporting MPs, however, has said that holding the vote after the delay had already entered international law "created serious legal doubts about the legal situation surrounding the extension".