A cross-party group of 30 MPs has urged Rachel Reeves to impose a wealth tax on Britain’s rich in next week’s budget rather than announce spending cuts that would hit the most poor hardest.

In a letter to the chancellor, the MPs – including the former Labour leader Jeremy Corbyn and his then shadow chancellor, John McDonnell – say she could raise £24bn a year from a 2% tax on wealth above £10m and lay the foundations for a fairer, more sustainable economy.

Reeves is exploring ways to raise billions of pounds extra in taxes at the budget to plug a shortfall in the government finances worth £40bn, required in order to avoid a “return to austerity” or her breaking a self-imposed fiscal rule to balance day-to-day spending with tax receipts.

Labour has committed not to increase taxes on “working people” by raising income tax, national insurance and VAT, and has promised to cap corporation tax on businesses at the current rate.

As an alternative, the chancellor has explored raising existing taxes on wealth, including through inheritances and capital gains, but has ruled out an explicit new levy on wealth.

But the signatories from Labour, including Diane Abbot, all four Green MPs, the Liberal Democrats, Plaid Cymru, the Social Democratic and Labour party and the Alliance party of Northern Ireland, as well as independents, argue that wealth is under-taxed in the UK and a new levy on the rich would generate a “large stream of revenue”.

The letter, organised by the campaign group Green New Deal Rising, says in contrast to the general trend, taxes on the very richest are only slightly more onerous than they were in the mid-1960s.

“This is deeply unfair and immoral: in an age of climate and economic crises, where public funds are desperately needed, it is necessary that we redress this imbalance. The transformative potential of taxes on extreme wealth is clear, and appetite for them is growing.”

The lobbying of the chancellor by the MPs coincided with the release of two polls showing a majority of voters would back an increase in wealth taxes to raise money for repairing Britain’s crumbling public sector.

Six in 10 people thought the government should prioritise raising more money through inheritance tax reforms over cutting public spending at the budget, according to the poll of more than 2,000 people by Opinium for the centre-left thinktank Demos.

And as few as one in 10 people said spending cuts should be prioritised. The highest backing for inheritance tax reforms was among Labour voters, at 74%, but a majority (53%) of Conservative voters also backed changes being made.

A separate poll of more than 3,000 adults by Opinium, commissioned by the Trades Union Congress (TUC), found 62% of voters were in favour of asking those “with the broadest shoulders” being asked to pay more taxes. By contrast, as few as 12% thought taxes on the rich should not go up even if it meant worse public services.

Paul Nowak, the general secretary of the TUC, said: “The chancellor should be encouraged by the level of public support – right across the political spectrum – for creating a fairer tax system.

“Voters want those with the broadest shoulders to contribute more – especially at a time when our schools and hospitals are under so much pressure.”

The TUC said there was also support for Labour’s manifesto tax increases. It said 79% of voters backed cutting NHS waiting times and increasing appointments by cracking down on tax avoidance and non-dom loopholes, while 65% supported an end to tax breaks for private schools to pay for new teachers.

Proposing a package of reforms to inheritance tax, Demos said about £2.6bn could be generated in the current tax year, or about £16bn over the parliament. Among the changes include a proposal to cut the current levy on inheritances above the tax-free allowance from 40% to 30% for estates under £1m, but an increase to 45% for those over £2m.

Dan Goss, senior researcher at the thinktank, said: “With a rate cut for working families and reduced tax breaks, this proposed package would almost double the support for inheritance tax. And no matter what party people voted for this year, a majority say the government should prioritise the reforms over equivalent spending cuts or borrowing.

“The research shows that there doesn’t have to be a trade-off in tax policy between raising revenue and attracting support. The government could get the public’s backing for reforms if they make the system fairer, and our proposals would do just that.”