For months there has been an apparently insurmountable obstacle to Angela Rayner going for the Labour leadership, should Keir Starmer find himself facing a contest.

The investigation by HMRC into the former deputy prime minister’s tax affairs has hung heavily over her since she was forced to resign last September over underpayment of stamp duty on her seaside flat.

But now Rayner’s allies are increasingly confident that the inquiry will be resolved before the May local elections – a moment of high peril for the prime minister – paving her way for a full return to frontline politics.

The Guardian understands that outstanding legal issues over the tax investigation are being ironed out by lawyers and the HMRC process is now approaching its conclusion.

Rayner is also on course to make about £100,000 from speaking engagements since she left government and her memoir, meaning she has earned enough to pay off her outstanding tax bill. It is, as yet, unclear whether she will also have to pay a penalty.

The Labour MP can now turn to the future of her party – and what role she might play in it. In a major intervention on Tuesday night, at the campaign group Mainstream’s Spring reception, she warned her audience that “the very survival of the Labour party is at stake”.

Since her departure from frontline politics, Rayner has mostly restricted herself to public interventions on policy – leasehold reform, workers rights and trial by jury – where she believes she can nudge ministers in the right direction.

Another was added to the list on Tuesday when she described Starmer’s plan to make it harder for legal migrants to gain permanent residency in the UK as “un-British”.

But it was her criticism of the prime minister – her staunchest since returning to the backbenches – that caught the most attention. She warned that his government was “running out of time” to show it could deliver the change people needed and must not just “go through the motions in the face of decline”.

As far as those in the room were concerned, the starting gun on a contest had been fired.

Some of Rayner’s colleagues were bemused by her delivering such a punchy speech just seven weeks before the local elections, but allies defended her decision.

The Mainstream event was originally scheduled for the week of the Gorton and Denton byelection, but Rayner felt that it would be unhelpful to deliver her message just days before voters went to the polls, and anyway she was out campaigning.

Now, she appears to be preparing for what many Labour MPs now feel is inevitable: a challenge to Starmer’s leadership after a devastating set of results in May.

“If we lose Wales, lose in Scotland, lose in London and all across the country then the response can’t just be to say ‘give us more time’. At that point, the party is going to act,” one senior Labour MP said.

Rayner’s allies stress that – although she is both the bookies favourite and popular with the Labour membership – she has no plans to engineer a scenario to directly challenge Starmer.

Instead, she would weigh up political and personal considerations – and the breadth of her support across the party – before deciding whether to run. Allies of Wes Streeting, also expected to be a contender, insisted he has no plans to trigger a contest, so it is unclear how one would then come about.

Some MPs say there could be 81 MPs – the number required under party rules – prepared to call for the prime minister’s resignation. Others insist there would have to be a stalking horse candidate willing to go over the top first. The possibility of a group of cabinet ministers urging him to go has also been discussed.

But Starmer has repeatedly made clear he would fight any contest, which Downing Street sources claim he would win. “Keir won a big personal mandate for change at the last election and he intends to deliver on it, however hard that may be,” one said.

The prime minister’s supporters believe there are enough MPs who don’t back any of his putative rivals to protect him from a contest and ensure that he stays in No 10. They also argue that many MPs are spooked by looking just like the Tories by ousting another prime minister.

Until recently, Rayner – publicly at least – agreed. She rallied round when Anas Sarwar called for Starmer to go last month, posting that Starmer had her “full support” and urging the Labour party to come together. With her intervention, any prospect of a coup was over.

But despite the public display of loyalty, allies suggest that Rayner has, over time, been losing faith in Starmer and his Downing Street operation – and thinks the party must now take a different direction.

Her early frustrations with some of the people around Starmer – who she is understood to have felt pushed him into poor political decisions – began to settle on the prime minister himself. “Angela couldn’t defend him any more,” one friend said.

His decision to make Peter Mandelson the UK’s ambassador to Washington was a turning point. The Guardian understands that Rayner had privately warned Starmer against going ahead because of Mandelson’s links with Jeffrey Epstein.

Across the Labour party, Rayner’s remarks on Tuesday night were interpreted as a rallying call to MPs. But she has also been engaging with the City in recent months, in an attempt to reassure that she would not lurch leftwards – instead sticking to Labour’s election manifesto and, crucially, Rachel Reeves’s fiscal rules.

“She talked about evolution, not revolution, and repeatedly mentioned how important stability was to her,” an attender at one event told the Guardian.

Rayner has also started to build up what some Labour MPs believe is a war chest for any leadership contest – receiving £72,500 in donations from Martin Littler, Trevor Chinn, Richard Greer and Refrigeration House since December, according to her register of interest.

The resolution of the HMRC investigation would remove the final impediment to her running – should a leadership contest take place. Many MPs feel the precariousness of Starmer’s position makes that all but inevitable.

Sarwar told Sky News on Wednesday that he had not changed his mind about Starmer needing to go.

Back in February, Labour MPs peered into the abyss, didn’t like what they saw, and stepped back from the precipice. Whether they do so a second time remains to be seen.