The Trades Union Congress has a modest proposal for Prime Minister Andy Burnham: bring back the bank surcharge, use the money for a "social tariff" on energy bills, and let two-thirds of British households breathe a little easier. Revolutionary stuff, we know.

TUC general secretary Paul Nowak made the pitch in a wide-ranging BBC interview ahead of the union body's annual congress in Brighton next week, arguing the government should introduce a social tariff - a discount on bills based on household income - paid for by reversing the bank surcharge cut. That surcharge was reduced in 2023 from 8% to 3% by the then Conservative government, and the TUC estimates restoring it would raise £9bn over four years.

"I think it will appeal to the prime minister," Nowak said. "These are policies that make a difference in the real world and people can see a value in them." He added that next month's Budget needed to show "the government is back in the service of the British people."

While Nowak said Burnham had got off to a good start as prime minister, he arrived with a series of "asks" for Burnham and the new Chancellor, John Healey. Top of the list: more help with energy bills. "We need to drive down inflation - those energy bills are fuelling inflation," he said. "And millions of families up and down the country are worried about turning on their heating this winter."

Burnham has already offered what he calls "breathing space" on the cost of living by temporarily scrapping VAT on electricity bills from October. Nowak reckons the social tariff idea would play well with Labour MPs, while the Liberal Democrats and the Greens in England and Wales have called for a windfall tax on banks too.

UK Finance, which represents well-known banks and lenders, begs to differ. The organisation suggests heavier levies would undermine the government's ambition to deliver "growth in every postcode" and damage international competitiveness, arguing UK banks already face a heavier tax burden than those in the US. So could the TUC's revenue-raiser be counter-productive and threaten finance jobs? Nowak is sceptical. "I can't believe banks would leave the UK just because we are restoring the surcharge to where it was in 2023," he said. "Bank share prices have risen faster here than in New York."

The TUC's tax demands don't stop at banks. Nowak argues the UK has "a tax system that's good at taxing income but not good at capturing wealth," and suggests a windfall tax on social media companies plus equalising Capital Gains Tax rates with income tax. The economist and former minister Lord O'Neill - who has advised Burnham - recently said wealth taxes were "the last thing that should be happening if we want to see more growth." Nowak's response: "With respect, I think he is wrong. I'm interested in a growing economy but a growing economy that works for everybody. It is right to ask those with broader shoulders to pay a fairer share."

Nowak also doesn't believe the government will deliver on re-industrialisation and its housing targets without making it easier to borrow to invest. As Chancellor, Rachel Reeves tweaked her so-called fiscal rules on debt and borrowing, but Nowak said the scope this provided for extra investment hasn't been maximised. "John Healey should leave no stone unturned in allowing us to invest in our economy, in our public services and in our national security," he said. "He should think about the flexibility he has got within those rules to make investments in the long term."

On immigration, the home secretary has announced a policy change that would see most migrants in the UK wait 10 years rather than the current five before settling permanently, with some care workers facing a 15-year wait. Before rejoining government, Angela Rayner argued it was "unBritish" to "move the goalposts" for those already working in Britain. A consultation on the proposed measures closed six months ago, and the government is yet to produce its response.

Nowak - a grandchild of migrants from Poland and Hong Kong - says: "We should think again not just for care workers but for workers right across the board. There are 111,000 staff vacancies in social care at the moment. It's important the rules aren't changed arbitrarily. I would hope and expect this and it needs to be the beginning of a grown-up conversation on immigration." TUC delegates will debate immigration next week and are likely to echo the call for the government to water down its changes for existing migrants.

Nowak said he felt it was right for Labour to change leaders after disastrous local election results in May, and has been pleased to see a bit of a "Burnham bounce" in the polls. But he warned the prime minister that he needs to provide "meaningful change" if he wants to see off an electoral threat from the populist Right. "The onus is on Andy Burnham to show he can deliver what he promised," he said. "If he fails to do it, there are people with glib answers who will turn this country into a more divisive place."