Angela Rayner has been cleared by HMRC of deliberate wrongdoing or carelessness over her tax affairs, the Guardian can reveal, paving the way for a potential leadership bid as Keir Starmer’s grip on power unravels.

The former deputy prime minister has settled £40,000 in unpaid stamp duty after initially paying the lower rate, but has not paid any penalty as a result of the investigation. HMRC was also satisfied there was no tax avoidance.

In an interview with the Guardian, Rayner said she had been “bruised” by the whole experience because of the intrusion into her disabled son’s personal life, but also because it had appeared as though she was “in it for myself” rather than on the side of ordinary people.

The investigation by HMRC into her tax affairs has hung heavily over the senior Labour MP since she was forced to resign from the cabinet last September. Now it has been resolved, the door is open for a return to frontline politics.

Rayner indicated she may run in the event of a contest, saying she wanted to “play my part” and that she understood why Labour MPs were so upset following last week’s election crushing. She said Starmer should “reflect on” stepping aside.

With Labour on the brink of civil war, Wes Streeting, the health secretary, is preparing to launch a leadership challenge on Thursday if he and his allies can secure the support of enough MPs to trigger a contest.

His move to force a race has sparked a frantic scramble on the left of Labour to find a candidate to oppose him, with Ed Miliband and Rayner both possible contenders, while Andy Burnham is unable to run from outside parliament.

Rayner suggested she could enter any leadership contest, should one be triggered by Streeting on Thursday, although sources have said she was not dead set on being the left’s candidate.

“I’ll play my part in doing everything we possibly can to deliver the change, because it’s not a personal ambition, I know the difference it makes,” she said when asked.

“Whatever role I can play, I will keep pushing and pushing hard because I want the people out there at the moment who are really struggling … to know that I’m putting all my energy into fighting for them.”

Rayner did not rule out endorsing a soft left rival if they had a better chance of success in any contest, raising the prospect of potential candidates on her wing of the party agreeing who would represent them.

“I don’t think it’s a case of each person for themselves, but I do think it’s a case of people seeing how they can pull the party together and have the vision to take us forward. You have to play your role as part of a team,” she said.

But Starmer’s former deputy ruled out launching a coup herself. “I’ve made it clear that I wasn’t going to trigger the prime minister – and that I want to see change. I want to see actions, not just words.”

Rayner declined to say whether Starmer should fight any leadership challenge, saying that was a matter for the prime minister. When pressed on whether he should step aside, she said: “Keir will have to reflect on that.”

She added: “I’ve said to Keir this is a really significant moment for our party and the country … The pace of change hasn’t been enough for voters to see, and also mistakes have really blown us off course and made voters doubt us.”

Streeting has been organising an attempt to oust Starmer for days since Labour’s disastrous election results, which Rayner said had left many MPs – including herself – “heartbroken” at losing longstanding councillors.

“Whatever Wes is doing, he has to justify his actions,” she said. “I do understand my colleagues and why they’re they’re angry and upset … I do understand why we’re having this conversation now, but we need to get through that as quickly as possible.”

Rayner again stressed that Burnham should not have been prevented from re-entering parliament.

“If somebody wants to come and help, and be part of the future that we can deliver, then absolutely we shouldn’t be blocking people … We cannot afford to be factional about this. We cannot afford to have egos,” she said.

But when asked, she said it would not be appropriate for her to ask Labour MPs in the north-west to stand down from their seats so that he could run.

Rayner’s last eight months have been overshadowed by the HMRC investigation, which was initiated after it emerged she had underpaid stamp duty on a Hove flat that she bought when her son’s trust bought her out of the family home.

“I felt that voters were left with the impression that I somehow tried to avoid – or worse had been reckless or careless – in my actions. Whereas now hopefully people can see that actually it’s a really complex area of law,” she said.

But she acknowledged that some people would still feel uncomfortable about a former housing secretary paying the standard rate of stamp duty, when HMRC said she should pay the higher one.

“Yeah, I understand that, but this is a very complex area of tax. It’s ambiguous and I did get advice at the time. Therefore I felt like I’d done everything I could to ensure that I complied,” she said.

However, she says the investigation had “clipped my wings” because it made people feel she wasn’t “on their side”. She added: “That hurt the most, yeah, because that’s what I’ve always fought for.”

Rayner consulted two leading tax lawyers on her affairs and they reached two different conclusions. One advised her she would have a “realistic chance” of successfully appealing against HMRC’s decision but that it could take years. She accepted the decision and paid the tax.

“Politicians should be held up to high standards and that’s why, when there was a question mark, I resigned from government. I think that was the right thing to do,” she said.

“It was just the constant digging and then headlines of ‘I avoided tax’, ‘I didn’t want to pay the tax’, or that ‘I’d taken money from my son’, all these insinuations, all these things that were not accurate.

“I’m relieved because the one thing that has really upset me is that the public thought in some way that I had either been careless, or that I’d tried to avoid paying tax, when both of those things are clearly not right.”