Rightwing Tories have met after Rishi Sunak sacked Suella Braverman as home secretary, with one MP publishing a formal letter of no confidence in the prime minister. Andrea Jenkyns, a noted supporter of Boris Johnson who served as schools minister under Liz Truss, tweeted her letter to the party’s backbench 1922 Committee, saying: “Enough is enough … It is time for Rishi Sunak to go and replace him with a ‘real’ Conservative party leader.” Braverman supporters stressed they did not expect significant immediate pushback against a cabinet that took a notable step to the centre with her departure and the unexpected return of David Cameron, but the former home secretary is unlikely to stay quiet. Shortly after Sunak sacked Braverman after accusations that her rhetoric had inflamed tensions over violent Armistice Day protests, the latest in a series of challenges to the prime minister’s authority, she said she would “have more to say in due course”. There is widespread expectation that she will unleash another eviscerating newspaper article, positioning herself as a figurehead for right-leaning Conservative MPs. The New Conservatives, a populist-leaning alliance of MPs led by Danny Kruger and Miriam Cates, met in parliament on Monday evening. One source said Braverman’s sacking was not on the official agenda, but “I doubt we will even get to item one” given the likely focus on the reshuffle. After the meeting, one MP said they had questioned whether the government was “going to embrace the realignment” of post-Brexit politics or not. About a dozen rightwingers in the New Conservatives faction, which included the party deputy chair, Lee Anderson, and Braverman’s ally Sir John Hayes, were said to be “far from pleased” as they gathered for a meeting in the Commons. However, they added that Braverman’s future did not come up during a “group counselling session” focused on policy and philosophy. One MP who supports Braverman said Sunak had misjudged both his MPs and voters by removing her: “Suella is popular. The political establishment might tut about her views on protests, but our constituents agree. Rishi might have created a problem for himself. She will become a rallying point.” Supporters of Braverman expect much of this to be focused on positioning for a likely post-election leadership battle, but some believe at least a few more MPs could be sufficiently disgruntled to submit no-confidence letters in Sunak. The direct trigger for Braverman’s removal was her article for last Thursday’s Times, in which she claimed there was a “perception that senior police officers play favourites when it comes to protesters” and were tougher on rightwing extremists than pro-Palestinian “mobs”. The article was submitted to Downing Street, but not all the edits sought were made. On Saturday, crowds of far-right activists fought with police near the Cenotaph as part of what was billed as a “counterprotest” to a vastly larger and generally less fractious demonstration in favour of a ceasefire in Gaza, with the Met police and Labour saying Braverman’s words had played a part in exacerbating tensions. After being sacked, Braverman said: “It has been the greatest privilege of my life to serve as home secretary.” The immediate response from most of her supporters in the parliamentary party was muted, although Jenkyns tweeted: “I support @SuellaBraverman. Sacked for speaking the truth. Bad call by Rishi caving in to the left!” Braverman has now been forced out of the same job twice in little more than a year. Liz Truss ordered her to resign in October last year after only weeks as home secretary, for sending confidential information to an MP from a private email address. She returned six days later, after Sunak took over in No 10. The shadow home secretary, Yvette Cooper, said Sunak should “never have reappointed her in first place”. She added: “He was warned against it and was warned on the damage she was doing. He went along with her undermining the police. Buck still stops with this weak PM.” The Liberal Democrat leader, Ed Davey, said: “Suella Braverman was never fit to be home secretary. Rishi Sunak knew this and he still appointed her. It was the prime minister’s sheer cowardice that kept her in the job even for this long.” Braverman was a key minister with a role in trying to deliver Sunak’s pledge to stop small boat crossings over the Channel, but she become involved in a series of rows, often irritating No 10 with her comments. She floated the idea of banning charities from giving tents to homeless people, saying they were “occupied by people, many of them from abroad, living on the streets as a lifestyle choice”. Recently she repeatedly labelled demonstrations calling for a Gaza ceasefire as “hate marches”. She had angered others by referring to the arrival of asylum seekers in small boats from across the Channel as “the invasion on our southern coast”. At October’s Conservative conference, Braverman made a notably populist speech attacking the “luxury beliefs” of liberal-leaning people, and prompted a Tory London assembly member to heckle her for making his party look “transphobic”.