Theresa May has drafted staunch supporter Amber Rudd back into the cabinet as the work and pensions secretary and took personal control of the final phase of Brexit negotiations.

The prime minister sought to shore up her support hours after Michael Gove decided to remain in the cabinet, despite having told her on Thursday he believed her Brexit deal was “not a runner” and will not get through parliament.

As the threat of a no-confidence vote rose, with ardent Brexiters gathering letters calling for her to be ousted, Downing Street sought to show it was business as usual, replacing ministers who had resigned in protest at her Brexit deal.

Amber Rudd's return is a surprising yet inevitable new dawn Read more

Rudd, who resigned as home secretary just seven months ago over the botched handling of the Windrush scandal, will now have to oversee the rollout of the controversial universal credit system.

After Gove turned down the job of Brexit secretary, May announced that junior minister Stephen Barclay would be given the role – but Downing Street said he would focus on domestic preparedness and piloting legislation through parliament.

With just over a week to go until the EU summit planned for 25 November, and the final details of the political declaration on Britain’s future trading relationship to be hammered out, Downing Street said the negotiations would now be “leader-led”.

Gove opted to remain in post after warning May on Thursday he would have to consider his position.

Friends of the environment secretary said he had become convinced the deal would not win the necessary support in the House of Commons after the hostile reaction from the Democratic Unionist party and many Tory backbenchers – and told the prime minister as much.

After considering his position overnight, Gove decided to stay, but he is now expected to band together with other Brexit-backing cabinet ministers, including Andrea Leadsom and Penny Mordaunt, to call for changes to the Irish backstop.

Downing Street has repeatedly insisted the withdrawal agreement is no longer open for negotiation, with just political declaration setting out Britain’s future trading relationship due to be hammered out in the next few days.

Rudd, who had described May’s Brexit deal as “exciting” earlier this week, immediately leapt to the prime minister’s defence against her backbench detractors, who are seeking to muster the 48 letters they need to secure a no-confidence vote.

“I would ask them to think again, this is not a time for changing our leader. This is a time for pulling together, for making sure that we remember who we are here to serve, to help, the whole of the country,” she said.

“I am worried that some of our colleagues are too concerned about the Westminster bubble, rather than keeping our eye on what our job is, to serve people.”

At least 23 Conservative MPs were known to have submitted letters of no-confidence to Graham Brady, chair of the backbench 1922 Committee, on Friday.

The former Brexit minister Steve Baker, who is orchestrating the challenge, suggested the target of 48, which would trigger a no-confidence vote, was likely to be reached over the weekend.

The shadow home secretary, Diane Abbott, reacted with fury to Rudd’s return to frontline politics so soon. She tweeted: “Amber Rudd resigned because of her mismanagement of Windrush scandal. Now Theresa May puts her in the DWP. Let’s hope she shows more concern for the victims of this department’s unfairness and cruelty than she did at the Home Office.”

Barclay, the MP for North East Cambridgeshire since 2010 and a Brexiter, had been a junior health minister since June 2017. A former director of Barclays Bank who trained as a solicitor and also worked as a financial regulator, Barclay was also City minister.

Among Rudd’s immediate tasks will be steering through the Commons the secondary legislation to allow the so-called “managed migration” of people still receiving some of the six benefits that universal credit replaces on to the new system, a huge task fraught with difficulties.

Rudd stepped down as home secretary in April after telling the home affairs committee that her department had no targets for deportations under the “hostile environment” policy, a claim swiftly disproved by documents leaked to the Guardian.

She was already under huge pressure over revelations about the treatment of members of the Windrush generation, people who arrived from the Caribbean decades before but were wrongly targeted for deportation and other sanctions because they could not prove their status.

It subsequently emerged that an internal Home Office report criticised senior officials for misinforming Rudd before her appearance at the committee amid a series of confusions and miscommunications.

May also lost a series of junior ministers and government aides amid the disquiet at her Brexit plans. As part of the reshuffle, the MPs Stephen Hammond, John Penrose and Kwasi Kwarteng were given junior jobs in the health, Northern Ireland and Brexit departments.

In an interview with Saturday’s Daily Mail, May acknowledged she had experienced a “pretty heavy couple of days”. However, she attempted to play down the impact on herself personally, saying it had been harder for her husband, Philip, to watch. “He does feel some of the hurt. We’ve been married for 38 years, that’s a long time. He is my rock.”

She said he had to turn off some of the critical coverage of her on the TV and had brought her a large whisky when she finished Wednesday’s five-hour meeting, where her cabinet gave their initial backing to the Brexit deal.