Sometimes a plan can be too successful. When Durham police announced on the day of the local election results that they would investigate Keir Starmer over ‘beergate’ – an event in April last year where Starmer was filmed drinking a beer with Labour staff, at a time when indoor socialising was banned – Tory MPs were delighted. After months of Starmer attacking the government for partygate and demanding Boris Johnson’s resignation, it was the Labour leader’s turn to face allegations that he broke Covid rules. ‘Delicious,’ as one member of government put it.

The initial hope in Conservative Campaign Headquarters was that a police investigation into beergate would silence Labour MPs’ calls for resignations and stop them scoring points from the sidelines. The Tories can claim some victory on that front: party-gate didn’t come up in the leaders’ exchanges following this week’s Queen’s Speech. Voters might conclude that Starmer and Johnson are as bad as each other. The first poll since the news of the Durham police investigation showed Labour’s lead over the Tories had dropped to just one point.

But since last week, Tory strategists have started to worry. What if Starmer actually resigned, as he has promised to do if he is fined? That would raise awkward questions about Johnson clinging on. Ministers doing the broadcast rounds were told to avoid questioning Starmer’s future and instead focus on the accusation that he is a hypocrite.

Starmer’s team believed he had no choice but to put his future in the hands of the police, since he has called not just for Johnson to resign but also Rishi Sunak, who was fined for the offence of turning up early to a meeting where birthday cake was served. The bet might pay off: Durham police have shown restraint in the past, as Dominic Cummings found out after his trip to Barnard Castle. The force concluded a ‘minor breach’ of lockdown rules may have happened, but no action would be taken. Labour sources say Starmer will stay on in the event of a ticking off from the police.

While Starmer’s supporters maintain his innocence and claim to have the evidence to prove it, they are still nervous about the investigation’s opaque process. ‘You just can’t be sure,’ says one Labour figure. By putting his job on the line, Starmer has forced his party to think about successors, whether now or later.

Tories regard Starmer as reliably dull: an opposition leader who has struggled to excite voters or capitalise on Conservative misery. ‘It’s better for us if we face Starmer at the next election,’ says a senior minister. ‘He is our best asset,’ agrees a government adviser. Johnson’s deputy chief of staff David Canzini’s main line of encouragement after significant Tory losses in last week’s local elections was that Labour ought to have done better, all things considered. An opposition that wins in Mayfair but loses in Newcastle-under-Lyme is not going to keep Johnson’s Tories awake at night.

There are those in the Labour party who would agree. The party made historic gains last week by taking Westminster, Wandsworth and Barnet councils, but did not do too well in the so-called red wall. While the bulk of MPs acknowledge that they are in a better place than they were two years ago, they are disheartened that the Liberal Democrats gained more council seats than they did. ‘This should be our moment,’ complains one Labour MP.

Those on the left say Starmer lacks a radical vision, but others argue he has focused too much on attacking the government for partygate and not enough on tackling the cost-of-living crisis. They also complain that he is too slow to react: it took several days for him to make his promise to resign if he received a fine.

A new leader could make things more difficult for the Tories. Johnson’s allies have long held the view that the Prime Minister finds it much harder going up against a woman than a man. The sense among Labour MPs is that the current favourite for the party’s next leader is Lisa Nandy, the shadow housing secretary, who is to the left of Starmer and would be likely to secure trade union support. For weeks she has been saying that the party should focus on the cost of living. If Starmer had taken her advice, rather than using partygate to argue about Johnson’s moral deficiencies, he wouldn’t be in such a mess. ‘Lisa has a knack for sounding reasonable but being radical,’ says a Westminster admirer. For his part, Cummings went so far as to urge Labour MPs last year to ditch Starmer for Nandy if they wanted to beat the Tories, arguing that the party ought to be led by a ‘woman from the Midlands who can focus on the public and build a team’.

Regardless, the bookies’ favourite is a northern man: Andy Burnham, the health secretary turned Greater Manchester mayor. After him there’s Angela Rayner, Labour’s straight-talking deputy leader. Given that Burnham has no seat and Rayner was at the same curry and beer evening as Starmer, neither seem particularly good bets should Durham police do their worst. Yvette Cooper, shadow home secretary, may stand again. Other potential candidates include Rachel Reeves, the shadow chancellor; Bridget Phillipson, the lesser-known shadow education secretary; Wes Streeting, the shadow health secretary; and David Lammy, the shadow foreign secretary.

The hard left would almost certainly try to field their own candidate. It’s notable that Jeremy Corbyn allies – such as Diane Abbott – were the first to say Starmer would need to go if he was fined. There’s no clear candidate yet, but names in the fray include the Corbyn-era shadow minister Barry Gardiner – nicknamed ‘Beijing Barry’ by his enemies since he admitted taking £500,000 in funding from a Chinese communist agent – and Zarah Sultana, a 28-year-old ‘heir apparent’ for Corbyn (Labour activists now sing ‘Oh, Zarah Sultana’ as they once did for the former party leader).

Even if Labour’s left unites around a candidate, it will be hard to repeat Corbyn’s 2015 insurgency. At party conference last year, Starmer tightened the leadership rules so that any candidate must have the support of 20 per cent of Labour MPs to run. Even under the old rules, a threshold of 10 per cent, Corbyn only managed to gain enough support thanks to sympathy votes from colleagues who didn’t expect him to win. No one will take that risk this time.

There are MPs who argue that Streeting – the 39-year-old centrist who once said he’d ‘snog’ Tony Blair – would fare better than Nandy in a general election. He is a career politician and seen as a rising star. In the role of shadow health secretary he has established a reputation as one of Labour’s best media performers. But he is still relatively unknown, so he could struggle to win union support, which would mean he would have to take the long route and secure nominations from local Labour parties. Like Reeves, the shadow chancellor, he may prove too centrist for the membership.

So both of Britain’s main parties are stuck with leaders being investigated by police for breaking Covid rules, but neither party has an obvious candidate for succession. Nandy is the option that Tories fear most. They believe she has more bite than her boss. When Durham police return their verdict, the Prime Minister and his opposite number may both have reason to hope that they find Starmer not guilty.