Britain's Prime Minister Theresa May takes questions during a press conference inside 10 Downing Street in London, Thursday, Nov. 15, 2018. Two British Cabinet ministers, including Brexit Secretary Dominic Raab, resigned Thursday in opposition to the divorce deal struck by Prime Minister Theresa May with the EU — a major blow to her authority and her ability to get the deal through Parliament. (AP Photo/Matt Dunham, Pool)
PHOTO: Matt Dunham/AP
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(CNN) —  

The beleaguered British Prime Minister Theresa May began to rebuild her splintered government Friday, replacing two Cabinet ministers who quit over her troubled Brexit plans and facing down demands that she resign.

After a rollercoaster week that threatened to bring an end to her premiership, May survived Friday without any further high-profile departures from her administration. To the relief of Downing Street, key Brexit-supporting ministers said they would stay on.

Crucially, May won the support of Michael Gove, a leading Brexiteer who was said to have been on the verge of quitting. “I am looking forward to continuing to work with all colleagues in government and in Parliament to get the best future for Britain,” he told reporters mid-morning.

Environment Secretary Michael Gove speaks Friday outside the Department for Environment, Food and Rural Affairs in London.
PHOTO: Victoria Jones/PA Images via Getty Images
Environment Secretary Michael Gove speaks Friday outside the Department for Environment, Food and Rural Affairs in London.

Another Brexit-supporting minister, International Trade Secretary Liam Fox, told CNN he would stay in the Cabinet, and urged fellow Conservative Party lawmakers to support May. “I think that we have to wait until we conclude this process,” he said. “I think the Prime Minister deserves the right to put that case to the European Union. I think that the greatest price that could be paid would be to have no Brexit at all.”

In a sign of May’s weakness, however, she did not deny reports that Gove had snubbed an offer to take up the post of Brexit Secretary, vacated by Dominic Raab in the most significant of Thursday’s bombshell resignations. “I had a very good conversation with Michael yesterday,” she told LBC Radio.

The specter of a confidence vote still looms over May. A total of 21 Conservative MPs have publicly demanded she step aside, short of the 48 required under party rules to trigger a vote. But more may have made their views known in private to party officials.

If a confidence vote is called, it could take place within a matter of days. If May lost, she would be forced to step down as Prime Minister and Britain’s political crisis would get considerably more intense. But if May wins, Conservative Party rules prevent another challenge for a year.

Amber Rudd, pictured in October, rejoins the Cabinet after resigning as Home Secretary in April.
PHOTO: OLI SCARFF/AFP/Getty Images
Amber Rudd, pictured in October, rejoins the Cabinet after resigning as Home Secretary in April.

In an attempt to shore up her government, May picked a key ally, Amber Rudd, to replace Esther McVey as Work and Pensions Secretary. Soon after, she appointed Stephen Barclay, formerly a health minister, as Brexit Secretary.

Rudd had resigned as Home Secretary in April after admitting she “inadvertently misled” MPs over deportation targets. A parliamentary report later ruled Rudd had been poorly served by officials.

She urged rebel-minded Conservative MPs to support May. “This is not a time for changing our leader,” Rudd said in a pooled broadcast interview. “This is a time for pulling together, for making sure we remember who we are here to serve, who we are here to help – that’s the whole of the country.”

Barclay, a Brexit-supporting junior health minister who has never served in the Cabinet before, is a loyalist who has not once voted against the government in parliament. His influence on Brexit negotiations is likely to be limited, as Downing Street announced that it will take the lead in further discussions with the European Union. Barclay will focus instead on getting Britain ready for leaving the European Union on March 29 next year.

It was unclear whether May’s opponents within her party would muster enough support over the weekend to force a confidence vote. Conservative Party chief whip Julian Smith – whose role is to maintain party discipline – was seen arriving at Downing Street on Friday morning as May seeks to rally support within Conservative ranks.

Conservative Party chief whip Julian Smith arrives at Downing Street on Friday.
PHOTO: DANIEL LEAL-OLIVAS/AFP/Getty Images
Conservative Party chief whip Julian Smith arrives at Downing Street on Friday.

Appearing on the LBC phone-in Friday morning, May maintained a defiant stance as she sought to sell her Brexit plan.

Asked why she believed she should stay on rather than standing aside to let a Brexiteer lead, she replied: “You’re absolutely right that for a lot of people who voted Leave, what they wanted to do was make sure that decisions on things like who can come into this country would be taken by us here in the UK, and not by Brussels, and that’s exactly what the deal I’ve negotiated delivers.”

Even if she survives a challenge to her leadership, May must still win approval for her deal from the UK Parliament – where she lacks a working majority. Few commentators think she has the votes to get her deal through, but all predictions about May’s capacity for survival have been wrong so far.

In Brussels, EU officials pressed ahead with preparations for a summit of European leaders on November 25 in to finalize and formalize the agreement. “Things are running on the right track here in Brussels,” one diplomat told CNN.

CNN’s Bianca Nobilo and Livvy Doherty contributed to this report.