Labour must “reunite the progressive voter coalition” if it is to take advantage of a split on the right and win the next election, the party’s deputy leader has said.

Lucy Powell, who won the race to be deputy leader 12 months ago with a warning that Labour was losing the fight to be heard as Reform UK surged, said the government now had a second chance under Andy Burnham.

In an interview with the Guardian, Powell said the party had clearly required a “change of leader” to revive its fortunes and tell a better story, after becoming “too technical and pessimistic”.

Labour’s improved poll ratings have led to speculation this week that Andy Burnham will call a snap election, but the prime minister rejected that on Friday and said the next contest would be in 2029.

However, the Labour conference will get underway this weekend with polls beginning to show for the first time in almost two years that Labour might be within touching distance of winning a majority at the next election – 12 months on from polls that suggested Reform UK could win a huge victory.

Powell said Labour was beginning to get a hearing again and should not be embarrassed to show its values clearly.

“If you look at the evidence from recent elections – right across the board – it’s clear that whichever party manages to unite its voter coalition is the one that wins. And for us on the left, that means bringing our centre-left bloc back together,” she said. But she added that “includes some who have considered Reform as they have lost faith in the status quo”.

She said Labour would bring progressive voters who had turned to the Greens, SNP or Plaid Cymru back to trusting Labour over the coming months and years – saying they had not always seen Labour as the best chance to defeat right-wing politics. “I’ve always thought there was a clear majority in this country who didn’t want the kind of politics of Reform and that divisive blaming of others – they didn’t like it,” she said.

“The challenge has been that sentiment has not all come to Labour and the progressive coalition was very, very fragmented. And part of our task and challenge is to reunite that progressive alliance and that voter coalition.

“I think we can. We’ve got red shoots of hope coming through. There are a lot more choices for people [when it comes to political parties] … but the task is to rise above that and to be the leaders of the progressive change.”

Ahead of her conference speech, the education secretary said she will use her new role to announce an expansion of anti-harassment work in schools, having called in her deputy leadership race for Labour to be more explicitly progressive especially calling out racism and misogyny.

She will say schools must go further than the strategy announced earlier this year to tackle misogyny, where pupils will learn about deepfakes, image-based abuse and online harassment.

Powell said schools would be required to “embed healthy relationships and belonging into every part of school life, not just RSHE [relationships, sex and health education] lessons” and show they were helping to create real-world, authentic community.

“We simply cannot just teach our way out of misogyny,” she said. “Schools with strengthened RSHE teaching but no wider culture shift will not shift attitudes.”

She said Labour was now “on the front foot” and the party would talk more boldly about choices like workers’ rights and free childcare hours.

“Let’s not be embarrassed about that, that’s what we are,” she said. “We lift children out of poverty, we take the difficult decisions in order to do that. I think at times we’ve been a bit worried about the reaction rather than just being clear about why we’re doing that.”

“There was a real strong desire for that clearer political communication. Of purpose, of story, of values. Andy knew that that’s what he needed to do. That was what the moment required,” she said.

Powell said it would be obvious under Burnham what Labour’s values were – suggesting he would not make the same missteps on issues like welfare.

“If we’re not for pensioner poverty, and we’re not addressing that, and we are not supporting people who need the safety net, then what are we for?” She added that the government under Starmer had “lost sight of some of the politics and the purpose” once they came into power.

“We have to be clear-sighted about what we’re doing, who we’re doing it for and clearly articulate that every single day.”

“It’s really encouraging to see that people are coming back. Andy’s shown that we can win in places like Makerfield against Reform, and in some key council byelections we previously lost to the Greens in May.”

Powell declined to agree directly with the chancellor, John Healey, that Burnham’s government was offering “continuity”. “We are on the same manifesto, but look I think people want change. We have to seize that opportunity of that second hearing to really punch home with that Labour story and the underpinning of why we’re doing what we’re going.”

Powell said she wanted to use the social media ban for under-16s as a moment to think about how to help young people to build real life communities that would replace the online world “so that people aren’t just accessing all their content and all their thoughts from social media … We’ve kind of ended up with this highly connected world where actually isolation has become a bigger feature.”