Suella Braverman has demanded “further action” against pro-Palestine marches, as centrist Conservative MPs expressed despair at Rishi Sunak’s delay in sacking his rogue home secretary. One senior backbencher predicted “a lot of noise” from angry colleagues when they return to parliament on Monday, with no signs of imminent action from Sunak after a series of controversies involving Braverman. Another MP said: “Every day she remains in office it further undermines the prime minister’s authority.” In her first public pronouncement since far-right groups fought officers near the Cenotaph, the home secretary made no comment on claims by Labour and the Met police that tensions had been inflamed in part by her own rhetoric. Condemning violence among both a large pro-Palestine demonstration and what she termed “counterprotesters”, Braverman focused on what she called “sick, inflammatory and, in some cases, clearly criminal chants, placards and paraphernalia openly on display” at the main march. Writing on X, she said: “This can’t go on. Week by week, the streets of London are being polluted by hate, violence, and antisemitism. Members of the public are being mobbed and intimidated. Jewish people in particular feel threatened. Further action is necessary.” Last week Braverman provoked fury after she ignored Downing Street’s request that she tone down an opinion piece for the Times, in which she accused the police of bias in how they deal with political protests. While her statement on Sunday was not in open defiance of Sunak, it indicated that Braverman is not minded to tone down language, which has dismayed a number of Conservative MPs. Ministerial social media posts are not normally vetted by No 10. The shadow home secretary, Yvette Cooper, accused Braverman of being “damaging and irresponsible” but the defence secretary, Grant Shapps, dismissed the idea the home secretary’s approach had emboldened far-right marchers, accusing Labour of “trying to play politics” over the issue. “The counterprotest was already going to happen,” he told Sky’s Sunday Morning with Trevor Phillips show. “Those people who were going to come and try and disrupt this weekend had already said they were going to do it.” Speaking on the same show, Cooper said: “Suella Braverman decided to launch an unprecedented attack on the impartiality of the police, and also to deliberately inflame tensions in the run-up to remembrance weekend. No home secretary has ever done that before.” Allies of Braverman, and a number of Tory MPs, believe No 10 is not minded to sack the home secretary immediately, especially given Wednesday’s supreme court ruling on the plan to deport asylum seekers to Rwanda, a key part of her policy brief. Some expect her to stay on until a reshuffle – even though other sources warn that Sunak could still act swiftly. However, the sense of indecision has alarmed Tory MPs who want her to be removed and who fear Sunak is too weak to stand up to her allies on the right of the party. There have been doubts over claims her allies number 50 or more. “I can see the logic of her staying for the Rwanda judgment on Wednesday, but if it goes much beyond that, it looks like she’s won the battle,” one backbencher said. “And no one wants to see their prime minister on the losing side.” Another said: “It’s not a surprise at all that this has been put on ice – if they’d wanted to sack her they would have done it already. It’s expected but it’s dismaying and it’s utterly shambolic.” A former minister said there was “despair” among many Conservative centrists, and that they were losing faith in Sunak. “Setting aside ethical issues, they just think all this is going to harm their electoral prospects,” the minister said. “The prime minister does seem to have a strange predilection, when any pressure appears, for deciding that these rightwing nutters should be accommodated.” In contrast, Braverman-backing MPs argue that examples of antisemitic placards and chants at the pro-Palestine event, which drew an estimated 300,000 crowd, vindicated her description of the demonstrations for a ceasefire in Gaza as a “hate march”. They also point to scenes on Saturday where Michael Gove was jostled and heckled by pro-Palestine demonstrators at Victoria station. The communities secretary tweeted on Sunday to thank police “for their exemplary work getting me home safely”.