Keir Starmer today pledges to defend public services from further austerity and protect working people from tax rises as he battles to stem a disastrous collapse in his party’s popularity ratings since the general election.

In an exclusive interview with the Observer before his first Labour conference as prime minister, Starmer moves to counter an impression of enduring “gloom and doom” and instead reassure increasingly restive Labour delegates heading this weekend to Liverpool that better times are around the corner.

He concedes, however, that leaks from Downing Street, particularly from staff angered by the influence wielded by his chief of staff, Sue Gray, are destabilising his administration less than three months on from the party’s landslide general election win.

“It is my job to do something about that and I accept that responsibility. And that just damages everybody,” he says, suggesting he wants to root out the leakers and restore unity to the heart of the Downing Street operation.

Labour’s gathering, which had been planned as a celebration of its election success, opens on Sunday with Starmer and his ministers facing an old-style union revolt on the conference floor on Monday over cuts to winter fuel payments, and the direction of economic policy.

The anger among some delegates has been compounded by disbelief at the way Starmer and his ministers have accepted “freebie” gifts, including clothes, from wealthy donors, inviting accusations that his so-called “government of service” is no different to the Tories.

After weeks of warnings about tough economic times ahead, as a result of the disastrous Tory management of the economy, Starmer went out of his way to make clear he was not about to usher in a new round of austerity.

In the interview, he insisted that public services were already starved of funds and could not take more cuts if they were to provide what the public needed: “I’m acutely aware that our public services are on their knees, and there will always be some that say there’s an argument for deep cuts … I ran a public service. I know what cuts feel like. And I know that a lot of them are cut to the bone. And therefore we have got to make sure that our public services are functioning properly.”

Looking ahead to chancellor Rachel Reeves’s first budget on 30 October, he was clear that working people would be shielded from tax increases. “People have had a lot of tax rises and there’s not much more room for tax rises. That’s why I made the commitment in relation to working people,” he said, referring to his election promise not to raise income tax, national insurance or VAT.

Having over recent weeks been at pains to emphasise the legacy left by the Tories – in the form a £22bn hole in the budget, broken prison system and an NHS on its knees – he made clear he now wanted to be more upbeat and explain how the Labour government intends to rebuild the country.

“I want to answer the ‘why’ question as well as the ‘what’ question … We do need to say why and explain and set out and describe the better Britain that this ladders up to.”

Ominously for Starmer, however, some of the biggest unions are working together on a conference motion demanding a reversal of Reeves’s hugely controversial decision to limit winter fuel payments to the poorest pensioners and more upfront investment in public services, as well as a wealth tax on the highest earners.

A vote on their motion could take place on Monday. The stance taken by the biggest union, Unison, at a meeting on Sunday could be crucial to the outcome of any vote.

An eve-of-conference opinion poll by Opinium for the Observer shows support for Starmer and his government has plummeted in just 11 weeks, at a speed that will cause deep alarm across the Labour party.

Starmer’s personal approval ratings have plunged to their lowest-ever – below that of the defeated Tory leader Rishi Sunak. They are down a massive 45 points since July.

While Labour continues to lead on most policy areas, its advantage on the key issue of the economy has collapsed to just one point, down from a 10-point lead in July. More than half of voters think the government has been bad at providing optimism or rebuilding trust in politics.

Sharon Graham, general secretary of Unite, delivers an uncompromising message to Starmer in an article for today’s Observer: “People need hope, not just gloom and doom. Nobody expected socialism, but some of us do expect some democratic challenges to the current inequalities of wealth and power. Otherwise, what’s the point?”

On the winter fuel payments, she condemns the prime minister for sticking by the policy: “Most people will forgive you for making a mistake. We all make them, after all. But doubling down? Refusing to change tack? Many will be less impressed by that.”

Starmer’s suggestion that he and ministers will not oversee a return to austerity comes amid signs that Reeves may be able to find some of the shortfall by other means.

She is known to be considering several measures that would free up funds for public investment, which under previous Tory budget proposals are due to be slashed over the next five years.

One possibility is that funds could be found through a reduction in the interest bill paid by the Treasury to the Bank of England which could hand No 11 up to £20bn a year, according to the New Economics Foundation.

Changes to the current fiscal rules could also give the chancellor more headroom.

On Sunday, Angela Rayner, the deputy prime minister, will announce measures to boost housebuilding, as Labour presses ahead with plans to build 1.5m homes within five years. She said: “We’ve inherited a Tory housing crisis. This Labour government is taking a wave of bold action to not only build the housing our country needs and boost social and affordable housing, but to ensure all homes are decent, safe, and warm.”