Labour MPs are calling for a close to the “endless drama” of leadership speculation, as Downing Street begins a fightback against predictions of an imminent challenge to Keir Starmer.

Some backbenchers warned that repeated briefings about how and when the prime minister could be toppled were putting off voters, who similarly had disliked the Conservatives’ repeated shuffling of leaders when in power.

“All people want is a government which works, and not the endless drama,” one MP said. “We are in a very tricky global situation, and to have this never-ending conversation about who might have a certain number of supporters feels extremely self-indulgent.”

Such worries are shared even among some Labour MPs who strongly believe that Starmer should be replaced. “You can both think the PM isn’t the right man to lead us into the next election and that now isn’t the right time to replace him,” one said.

Labour is expected to fare very badly in Thursday’s elections to the Scottish and Welsh parliaments and councils across England, with losses well above 1,000 council seats seen as potentially triggering a challenge.

Andy Burnham, the Greater Manchester mayor, has been widely linked with a planned return to Westminster, but faces a series of logistical hurdles, while the other two obvious candidates, Angela Rayner and Wes Streeting, are seen as not yet about to act.

Within the vacuum of what one MP called “a Mexican standoff”, allies of various camps have been briefing journalists, something which MPs not involved in the plotting say has become an intense annoyance.

“Most sensible MPs are out on the doorsteps, and aren’t worrying about all this,” another backbencher said.

“It’s all focused on personalities and not policy. We’re getting a lot of the ‘who’, but none of the ‘what, why and how’, which is what matters. The same thing with slightly better comms is not going to cut it.”

Some allies of Starmer worry the open plotting could make the results even worse, pointing out that in the run-up to the local elections, the group that represents Labour councillors told ministers that they needed unity to prosper.

“It’s less than a week from the elections, and we have briefings every day from some would-be candidate or another,” one said. “Nothing makes a party look more out of touch than this level of self-indulgence when people are really worried about the cost of living.”

There is, nonetheless, a definite sense among many MPs that Thursday’s elections could become a trigger, with one saying the expected losses would take things into “uncharted waters”.

“People have agreed it’s not working right now, but there isn’t an agreement on what is needed to make it work,” another MP said.

“Those that believe this is just midterm pains have factored in us losing 1,000 councillors. If we lose more, they may start thinking this isn’t normal – and I dare say they are right.”

Others, however, believe that, given the huge economic uncertainty of the Iran war, nothing should happen for at least several months. Some MPs have started to push for assurances that Rachel Reeves will be kept as chancellor whatever happens, to avoid spooking the financial markets.

Writing in the Observer, Starmer hinted at such worries, saying that during an earlier global crisis, with Covid, the then-Conservative government “descended into political infighting”.

Anna Turley, the Labour chair, was more explicit, telling the Sunday Mirror that Labour MPs should “be resilient” and stick with Starmer, adding: “Let’s not get distracted. Let’s not keep looking at ourselves.”

Speaking to the BBC on Sunday, Heidi Alexander, the transport secretary, echoed this argument.

“Asking the prime minister to somehow reapply for his job when all of that is going on and he is entirely focused on the concerns of the British people would be the wrong thing to do,” she said.

“Those people who think that we should have a leadership election now and repeat the mistakes that the Conservative government made in churning through prime ministers probably do need to give their head a gentle wobble.”