At midday on Saturday, hundreds of thousands of people will gather outside Hyde Park in London for what organisers say will be the biggest pro-Palestinian march since the Israel-Hamas war broke out just over a month ago. The marchers will hope their calls for a ceasefire in Gaza put pressure on the British government to do the same. But even before they have taken a step, the protesters have triggered political crises for both of Britain’s largest parties, leaving the Labour leader, Keir Starmer, looking weaker than he has for months and the home secretary, Suella Braverman, facing the sack. “I’m not sure if they meant it but this demonstration has managed to cause major crises for both parties,” said one Labour MP. “Which is impressive given it hasn’t even happened yet.” For Rishi Sunak, the week was supposed to be about him. The prime minister oversaw his first king’s speech on Tuesday, launching a series of bills on everything from tenants’ rights to smoking, as he sought to reinvigorate his party before a likely election next year. Instead, it is his home secretary who has dominated the headlines, first calling homelessness a “lifestyle choice” and then openly criticising the Metropolitan police for allowing this weekend’s protests to go ahead. Her words have irritated many on the Tory benches, who believe she is positioning herself for a leadership bid should the Tories lose the next election, and some of whom have jokingly nicknamed her “Cruella”. It is the way she has gone about courting attention that has particularly irritated Downing Street. Hours after Sunak made clear his backing for the Met’s decision to allow the march on Saturday, the Times ran a controversial article by Braverman accusing the police force of being biased towards leftwing causes and comparing the marchers to dissidents in Northern Ireland during the Troubles. What was worse for Sunak’s advisers was that they had demanded major changes to the piece, only to find it had been published largely in its original form without several of their edits. Downing Street said on Friday that Braverman retained the prime minister’s confidence, but officials are investigating how the article came to be published in that form, and Sunak is reported to be considering a formal investigation into whether Braverman broke the ministerial code. For many Tory MPs, the row typifies the way in which Braverman has repeatedly tried to weaponise controversial issues to bolster her rightwing credentials before what many expect will be a leadership contest after the next election. Many are getting so exasperated that they are calling into question whether she would have the parliamentary support to get into the final two in such a contest. “People are just tired of it now,” said one senior Tory MP. “She’s pissing everyone off.” Some believe Sunak was already planning to move Braverman in a reshuffle that could come as soon as next week, and that her latest manoeuvres are designed to make it look as if she has deliberately prompted it. “She is trying to make it look like she made it happen (or can prevent it with pressure), rather than she was just sacked for her current mess,” said one Conservative backbencher. Braverman still has her close allies, including John Hayes, Miriam Cates and Jonathan Gullis. But what has annoyed many of her otherwise sympathetic colleagues is the way her actions have overshadowed what should have been a bruising week for Labour. For all the divisions that Saturday’s march has triggered among Conservatives, the situation is more serious on the Labour benches, where many MPs are under heavy pressure from their members and constituents to back a ceasefire. Those tensions came to a head this week when Imran Hussain resigned as a shadow minister in the levelling up team, saying he wanted to be a stronger advocate for a ceasefire. Labour whips are watching more than a dozen other shadow ministers for signs they might resign, with the weekend’s march and an expected parliamentary vote on a ceasefire next week expected to prove flashpoints. Labour MPs say they are mostly willing to comply with an instruction from the leader’s office not to attend Saturday’s march. They will find it harder to vote against a likely motion by the Scottish National party calling for Israel to end its military campaign in Gaza. Party whips are so worried about a potential vote that they are spending the weekend calling Labour MPs around the country asking whether allowing them to abstain on the vote would be enough to ward off a rebellion. With Labour now more than 20 points ahead in the polls, potential rebels insist they do not want to bring down Starmer. A mass rebellion by his frontbenchers would challenge his authority on a scale unseen since the early days of his leadership, when he took on and expelled many on the left of the party. For all the angst within both parties over how to respond to fast-moving events in the Middle East and the reaction back home, polls suggest most voters are not particularly engaged with the issue. “Voters are evenly split on whether their sympathies lie more with Israel or the Palestinians,” said Anthony Wells, the head of UK political research at YouGov. “But there are a lot of ‘don’t knows’, and the salience is low. This is much more of an internal issue for political parties than it is one for voters generally.” Bronwen Maddox, the chief executive of the Chatham House foreign policy thinktank, said: “For all the traditional support for the Palestinian cause within Labour that has given Sir Keir Starmer recent trouble, the challenge of policy and tone for both main parties is similar.” The positions of Starmer and Braverman are likely to become a lot clearer on Wednesday. That is the day any parliamentary vote on a ceasefire is likely to be held, and by chance it is also the day the supreme court is due to decide on whether Braverman’s policy of deporting asylum seekers to Rwanda is lawful. “Come Thursday we should know whether Starmer has enough authority in his party to face down rebels over Gaza, and whether Sunak has enough in his to sack his home secretary,” said one MP.