Images are unavailable offline. British Prime Minister Theresa May speaks during Prime Minister's Questions in the House of Commons, in London, on Jan. 9, 2019. Jessica Taylor/The Associated Press

British Prime Minister Theresa May is rapidly losing control over her Brexit strategy after the government suffered a pair of humiliating defeats in the House of Commons this week – empowering parliamentarians and opening the door to another referendum on Brexit.

Britain is set to leave the European Union on March 29, and Ms. May has been trying for weeks to win support among members of Parliament for a Brexit agreement she struck with the EU in November.

Now, a group of MPs from all parties has won backing for a pair of motions that severely limit Ms. May’s Brexit plans and allow Parliament to consider a range of alternatives if her deal is rejected in a vote in the House of Commons on Tuesday. The move essentially means that control over Brexit has begun to shift from the Prime Minister to MPs.

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Ms. May has already delayed the vote once, hoping to win more concessions from the EU that would make her agreement more palatable to Tory rebels. But there is little indication that many MPs have been swayed and the deal is almost certain to be defeated on Tuesday. Ms. May had been hoping to have up to 28 days to come up with a new agreement or an alternative Brexit plan if her deal is voted down.

That deal includes a 585-page withdrawal agreement that outlines the terms of Britain’s departure, and a 26-page declaration that sets out a framework for future negotiations on a broad agreement covering trade and a host of other issues. But the deal has run into fierce opposition among MPs, particularly from a group of Ms. May’s fellow Conservative Party colleagues who support a hard Brexit, which would entail cutting almost all ties to the EU.

On Wednesday, MPs approved a motion that will force her to return to Parliament with a “Plan B” within three sitting days of Parliament, or Monday Jan. 21. MPs from all sides will also have the power to amend any second plan Ms. May presents. That clears the way for MPs to propose everything from a second referendum on Brexit to delaying the country’s departure from the EU and even cancelling Brexit altogether.

The MPs also won support for a motion that will force the government to seek parliamentary approval for some spending plans if Britain leaves the EU without a Brexit deal. “This solidifies and emphasizes the key role of Parliament,” said Tory MP Dominic Grieve, who spearheaded Wednesday’s motion.

The moves add more uncertainty to the Brexit process, which has already been thrown into question. With less than three months before Britain leaves the EU, there is no indication the country will have any arrangements in place, with the EU governing issues such as border controls, banking relations and even whether Britons will be able to use their cellphones in Europe. Several business leaders have expressed concern about a “no-deal Brexit,” saying it could cause economic chaos, and many companies have been stocking up on supplies.

Ms. May has insisted that if her deal is rejected, the country would be entering “uncharted waters,” and she has urged her opponents to come up with an alternative. Groups of MPs have raised several options, including a Norway-style arrangement that would see Britain remain outside EU institutions, such as the European Court of Justice, but within the European single market, which provides for the free movement of goods, services and people. Others have proposed a referendum asking voters if they prefer Ms. May’s deal or remaining in the EU. Still, more have suggested the country leave without a deal and then negotiate a trade agreement. Labour Leader Jeremy Corbyn has said he will push for an election.

Complicating matters is that there does not appear to be a clear majority for any alternative. That could yet play into Ms. May’s hands as she hopes a fractured Parliament will leave her deal as the only viable option. “The only way to avoid ‘no deal’ is to vote for the deal,” she told MPs on Wednesday.

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But she has little room to manoeuvre. Her Conservatives don’t hold a majority of seats in the House of Commons and she has to rely on the support of the Democratic Unionists, a Northern Ireland-based party that holds 10 seats. The DUP has come out against Ms. May’s Brexit deal, however, virtually assuring it will be defeated. The Tories are also deeply divided. Around 20 Tory MPs defied the government and backed the two motions this week and at least 40 hard-Brexit Tories have vowed to vote against the deal on Tuesday.