It is nearly eight months since Angela Rayner quit the cabinet because of her tax arrangements, but some might argue her influence on the government has not gone away. And soon she might return, whether as Keir Starmer’s saviour or, perhaps, his usurper.

There is increasing speculation that the prime minister could carry out a small-scale reshuffle, primarily to bring back Rayner, his former deputy and one of Labour’s political heavyweights.

This is by no means certain: Starmer is understood to have not yet made up his mind, and events depend in part on how significant a blow Labour is dealt in next week’s elections to the Scottish and Welsh parliaments and to councils across England.

Robert Hayward, the elections analyst and Conservative peer, has predicted Labour will lose 1,850 council seats on 7 May, above the 1,500 figure cited in one report as the possible trigger for a cabinet revolt. Adding to the sense of dread, Hayward’s forecast says Reform UK will gain about 1,550 councillors and the Greens 500.

If Starmer were to limp on after such losses, the temptation would be strong to get the cabinet support of Rayner as part of efforts to reset his government and signal to restive MPs that a change of direction is afoot.

Since she was forced to resign last September because of the underpayment of stamp duty on a flat, Rayner has walked a line between loyalty and interventionism, regularly reminding Labour colleagues of her policy ideas.

Some of her interventions have been seen by No 10 as helpful, such as her compromise on the workers’ rights bill she had spearheaded to help get it through the Lords.

Others have been viewed less favourably, such as her decision last month to label as “un-British” proposed changes to immigration rules, in a speech in which she also said Starmer could not “go through the motions” in the face of ebbing support.

Throughout this period, there has been regular speculation about a return to the frontbench, with Starmer himself saying he would welcome it. He and Rayner reportedly discussed the idea when they both visited a school this month.

The idea has, however, been obstructed by an ongoing investigation by HMRC into the stamp duty underpayment. Allies of Rayner had been confident the matter would be resolved before next week’s elections. If this timetable has slipped a bit, they still believe it will not drag on much longer.

There is, of course, one final hurdle: whether Rayner would want to rejoin what she may see as a sinking ship. There are certainly some in government who wonder if recent interventions, notably on immigration, mean she is more interested in making trouble for the government than joining it, and that her sights are set on replacing Starmer.

It is understood that she would listen seriously to any offers and would not demand to be made deputy PM again – David Lammy now fills the role – but most likely would refuse a “non-job”.

“She is not trying to be hostile,” said one minister. “There are people who weaponise her for their own purposes, but she wants to play a role again in frontbench politics.”

It is also the case that some of Rayner’s more pointed interventions, for example her critical speech last month, have expressed sentiments shared by many other Labour MPs. Others point out she can connect with voters in a human way, which Starmer seems unable to do.

There are some, however, who wonder if whether might not be more of an asset as a backbench MP, giving her the time to campaign and speak around the country. “She’s enjoyed getting out of the bubble a bit more,” one MP said.

All the calculations are filtered through the idea of whether – or, more likely, when – Starmer faces a leadership challenge, with Rayner routinely cited as a possible challenger.

One of the many moving parts in this would be whether another possible challenger, Andy Burnham, the Greater Manchester mayor, returns to parliament.

Speaking to Bloomberg at a conference in Spain, Burnham said the aftermath of next week’s elections would have to be “a moment of reflection” for Labour, which would involve “starting to now pull through on a different course”.

In January, Burnham was blocked from standing in the Gorton and Denton byelection, which Labour then lost to the Greens, and there is much speculation about whether he may try again.

In his comments to Bloomberg, Burnham praised Starmer but said he could try again to return as an MP. “The politics we’ve pioneered as mayors – place-first, not party-first – that needs to go national, and so we do need to reform Westminster,” he said. “I can’t remove the kind of feeling that some day I will try and go back. I’m not ruling it out.”