Rishi Sunak is being warned by senior Tories not to allow “Treasury orthodoxy” to choke off critical funding this winter, with Conservatives demanding action in the budget over energy bills, criminal justice and support for the low-paid.

As the chancellor prepares to unveil his budget and spending review this week, he is still being pressed to include measures that would curb the impact of rising energy bills and the GBP20-a-week cut to universal credit.

Sunak is set to announce a significant increase in the national living wage, and is also considering additional help for people struggling with energy bills in the wake of rising prices. His package will include GBP3bn for post-16 education and adult learning. It will cover skills boot camps, GBP1.6bn for teenagers to study T-levels, and 24,000 traineeships.

However, MPs from across the party are concerned that the Treasury is taking too hard a line on spending, which risks damaging Boris Johnson’s pledge to “level up” the country.

With Labour on Sunday calling for VAT on heating bills to be scrapped this winter, Robert Halfon, the Tory chair of the education select committee, said the move would help people through the winter and meet a Brexit campaign promise to cut tax on energy bills.

“This is a simple way of trying to alleviate the pain of ever-increasing energy bills for hard-pressed workers,” he said. “It’s a relatively small measure and will help people at a difficult time.”

Labour said a six-month suspension of VAT on domestic energy bills, currently set at 5%, would cost about GBP1bn and could be funded through higher than expected VAT receipts this year. However, Whitehall sources have warned such a blanket move would cut bills for the wealthy. The chancellor could prefer a more targeted scheme, such as an extension of the warm homes discount aimed at the low paid.

Sunak is also facing an attempt by peers this week to force a Commons vote on his decision to cut universal credit payments by GBP20 a week.

Sir Iain Duncan Smith, the former Tory leader who is pushing for Sunak to mitigate the impact of the cut, said: “We are not in the same situation as we were in 2010. We shouldn’t think of ourselves as in a Treasury orthodoxy, which is that we somehow have to claw back [spending] straight away. This is more like a war debt. Universal credit is about people’s lives. If you help support them, they pay you back.”

The pleas come amid growing warnings of a cost of living crisis. A typical family with two children would be almost GBP500 worse off next year from changes to national insurance alongside an expected 5% rise in council tax, according to new analysis by the IPPR thinktank.

A report by the TUC also shows that wages are not rising fast enough to offset higher tax bills and inflation. With wages rising annually at 3.5% to 4% and inflation heading to 5% in the new year, according to the latest assessment by the Bank of England’s chief economist, wages will begin to fall in real terms even before the tax rises take effect in April.

TUC boss Frances O’Grady said that reports from unions with members across the manufacturing and transport industry showed that outside a few sectors suffering acute shortages of labour, wage rises remained subdued.

A group of leading thinktanks and more than 70 academic economists are also using an open letter to urge Sunak to introduce a fiscal stimulus worth at least GBP70bn in his budget and spending to aid levelling up, rather than retrenching. Signatories include Simon Wren-Lewis, emeritus professor of economics at Oxford University, Professor Ha-Joon Chang of Cambridge University, and Diane Perrons, professor emerita at the London School of Economics.

There is also Tory concern that the criminal courts budget could again be hit, just as the National Audit Office warned that a backlog of cases in England and Wales is likely to persist for several years.

Robert Buckland, who was justice secretary until last month, told the Observer the justice system’s reputation was at stake.

“We’ve made good progress in the last few years increasing budgets in the Ministry of Justice, but it is important that it is sustained,” he said. “For a sum that is much smaller than the sums being spent on health, a lot can be done to restore the reputation of the justice system.”

Lord Mackay, who served as a Tory lord chancellor for a decade, said he had been growing increasingly concerned about the state of the justice system as a result of spending cuts. “I’m very strongly of the view that it’s extremely dangerous for us as a nation if the criminal work gets far behind,” he said. “If anything is done to make it worse, it would be a more serious breach of our responsibility to our people, including, the responsibility that we have under the Human Rights Act.”

A Treasury spokesperson said there was already an energy price cap for bills and a GBP500m household support fund to help those struggling the most. “The budget and spending review will set out how we will continue to invest in public services, businesses and jobs while keeping the public finances on a sustainable footing,” they said.