The leader of Britain's trade unionists has told Andy Burnham the government should introduce a "social tariff", paid for by a bank surcharge, to help low and middle earners with their energy bills.

A social tariff is a discount on bills based on household income, and the TUC says it believes two-thirds of households could benefit.

The TUC says the bank surcharge, which was reduced in 2023 from 8% to 3% by the then Conservative government, should be reversed – and estimates it would raise £9bn over four years.

TUC leader Paul Nowak said: "I think it will appeal to the prime minister. These are policies that make a difference in the real world and people can see a value in them."

In a wide-ranging BBC interview ahead of its annual congress in Brighton next week, the TUC general secretary said next month's Budget needed to show "the government is back in the service of the British people".

While he said Burnham had got off to a good start as prime minister, he had a series of "asks" of the prime minister and the new Chancellor, John Healey.

Top of his list is more help with energy bills, saying: "We need to drive down inflation – those energy bills are fuelling inflation.

"And millions of families up and down the country are worried about turning on their heating this winter."

Burnham has already offered "breathing space" – as he calls it – on the cost of living by temporarily scrapping VAT on electricity bills from October.

Nowak said the proposal for a social tariff would be popular with Labour MPs; while the Liberal Democrats and the Greens in England and Wales have called for a windfall tax on banks too.

However, UK Finance, which represents well-known banks and lenders, has suggested that heavier levies would undermine the government's ambition to deliver "growth in every postcode" and would damage international competitiveness.

The organisation argues that UK banks face a heavier tax burden than those in the US, for example.

So could the TUC's revenue-raising measure be counter-productive and threaten jobs in finance?

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. Bank share prices have risen faster here than in New York," he said.

The TUC's demands for tax-raising measures don't stop with the banks, with Nowak arguing the UK has "a tax system that's good at taxing income but not good at capturing wealth".

Nowak suggests a windfall tax on social media companies and for the government to equalise rates of Capital Gains Tax with income tax.

The economist and former minister Lord O'Neill – who has advised Burnham – said recently that wealth taxes were "the last thing that should be happening if we want to see more growth".

Nowak responded: "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."

In addition, Nowak says he doesn't believe the government will deliver on re-industrialisation and on 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 he believes 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 says.

"He should think about the flexibility he has got within those rules to make investments in the long term."

Nowak has another ask of the government.

The home secretary has announced a change in policy which would see most migrants who are in the UK wait for 10 years rather than the current five before they can settle permanently. Some care workers may have to wait 15 years.

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 says 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.

And the TUC head warned the prime minister that he needs to provide "meaningful change" if he wants to see off an electoral threat from the populist Right.

He says: "The onus is on Andy Burnham to show he can deliver what he promised.

"If he fails to do it, there are people with glib answers who will turn this country into a more divisive place."