Labour’s deputy leader has warned there will be “no magic bullet” to solve Labour’s problems – or major challenges facing the country – as its MPs grapple with how to navigate the fallout out from the local elections.

Lucy Powell told the Guardian she understood there was “huge anger and despondency” from Labour MPs in the aftermath of the Peter Mandelson vetting scandal, but said the prime minister would not make a similar mistake again.

Powell, who called for Keir Starmer to be more explicitly progressive during her deputy leadership campaign, said she would not engage in leadership speculation with the party facing a potential loss of more than 75% of the council seats it is defending, as well as losing power in Wales and failing to beat the SNP in Scotland.

But she warned restive MPs there would be “no one change” that would lead to a reverse in fortunes. “There’s no magic bullet here for us. We are in a difficult world,” she said in an interview on the campaign trail in Leeds, where the party is facing off against both Reform and the Greens in different parts of the city.

“I strongly believe that we’ve got the right agenda to start turning that around. To give people hope, an opportunity and see the change in their communities.”

Asked if Keir Starmer was the right leader to deliver it, Powell said: “I’m not going to get into that. I think there’s no one change that [will affect] all of these situations. We’ve still got to tackle these big issues, and we’ve got to do it in the right way with the right values. Having some side order conversation about personnel and people, I think misses the point.”

Powell, a close friend and ally of Andy Burnham, who is reportedly preparing a leadership run, said she knew the stakes were very high for the country. “If we get that wrong, then Nigel Farage is walking into Downing Street. We can all pretend that one switch over here would magically transform that. I just don’t believe that,” she said.

Powell said she hoped the country could now begin to move on from the Mandelson scandal, having spent the early part of last week ringing MPs to try to shore up support for Starmer ahead of the privileges committee vote.

“There’s a huge amount of anger, sort of despondency, I think. Every day that we’re still on the fallout from the Mandelson appointment is a day we’re not talking to our communities and our voters about what all our MPs and councillors want us to be talking about,” she said.

Powell said she had always distrusted the former US ambassador, who was sacked after new revelations about his friendship with convicted child sex offender Jeffrey Epstein. “I don’t like the way he operates, it’s always all about Peter, and I don’t trust his judgment either. That’s a view I’ve long held. Not everybody held that view. He’s not someone I would have even countenanced personally, but, that’s mine and his history,” she said.

But she said she believed that No 10 was now a different operation, with the departure of several influential aides who had been key to appointing Mandelson.

“Prime ministers do make hundreds of decisions. And they don’t get them all right. This one Keir got wrong … It does speak to an era, some people call it ‘the boys club’, but a culture there in Downing Street, in our politics.

“There has been quite a big move away from that and a recognition that the government was needing more differing views and opinions. Even in exactly the same circumstances. I don’t think that same decision would be made now.”

Starmer is thought to have rejected the idea of a wider reshuffle after the May elections as a way of trying to cement his position by bringing back soft left figures such as Powell and the former deputy leader, Angela Rayner, back to the full cabinet.

But Powell said she preferred her role to be solely political. “I’m personally quite sceptical about reshuffles as a device. We need to be governing for the whole country. We need to be governing as one Labour party, bringing together all the different groups and factions in the Labour party,” she said.

“But we also need to have a much stronger sense of politics. I’ve chosen to do this job entirely politically. I think I’ve made actually more impact doing it that way.”

Powell said that she believed the party could do better than the polls were predicting – and that Mandelson was not the major issue on the doorsteps, but whether Labour could really deliver change.

“I think we have the best ground campaign by a mile in this country. There’s a lot at stake. I’m not really in the expectation management business. But what I think people find is that on the actual doorsteps, there are different conversations to be had.

“There’s a lot of voters still quite unsure, especially in more Green-facing areas. I think it’s very soft. All our amazing members and activists – they’re very motivated to have those conversations.”