A former Conservative leader has called for benefits to be immediately increased to help the poorest cope with the cost of living.

But Iain Duncan Smith‘s plea came as two cabinet ministers spoke out publicly against bringing in a windfall tax on oil and gas companies to help pay for support for people struggling.

In an interview with the Sunday Telegraph, Northern Ireland Secretary Brandon Lewis said it would “put off investment” while Health Secretary Sajid Javid told Conservative activists in Wales he instinctively didn’t like it.

Chancellor Rishi Sunak has refused to rule out the idea, with one newspaper on Sunday reporting a staggered version of the levy is being looked at.

Sir Iain had told Sky News there should also be tax cuts for those in work to help “the squeezed middle”.

He said: “During the course of this spike we should make sure we bring those benefits that are relevant to those people who are in need up to be able to afford to pay bills that are going to be higher.”

Universal credit and other benefits rose by 3.1% last month, in line with the CPI rate of inflation in September last year.

This week inflation hit a 40-year high of 9% in the 12 months to April.

Amid spiralling prices, the government is under pressure to take further action with splits over the potential to raise money through a ‘windfall tax’ on the profits of oil and gas companies.

The Sunday Times has reported the chancellor is “attracted” by the idea of a “pro-investment” form of the levy which would offer different rates of tax depending on how much a company was prepared to invest in the UK.

A Treasury source pointed to previous comments made by Mr Sunak in which he said no options were off the table provided they lead to “significant investment back into the UK economy” and support “energy security”.

But there is hostility to the idea of ‘windfall tax’ within government with several cabinet ministers known to be against the idea.

Former Tory minister John Redwood has previously told Sky News “Labour’s windfall tax” was not needed because North Sea oil and gas “already pays double tax”.

He called on the Treasury to use increased VAT receipts to raise benefits and cut broader tax rates.

Read more: Four charts that explain what’s happening with inflation

Another former minister said the “gut instinct” for many in the Conservative party would be to help people through tax cuts but also acknowledged that “may be turned on its head” given the direct interventions that had taken place during the pandemic.

A newer intake MP said he had sympathy for the idea of increasing benefits but said that could only happen “if economy is strong enough to pay for it” and added that won’t happen “if we have taxed it to death”.

The government is already handing out £150 council tax rebates for many homes and will take £200 off energy bills from October.

Sir Iain Duncan Smith’s comments come as the think tank he founded – the Centre for Social Justice – called for benefit rates to be reviewed quarterly rather than annually and for tax cuts to be implemented for working people who claim Universal Credit.

Last week the chancellor said he was not able to raise the payments more than 3.1% due to an old computer system that the Department for Work and Pensions uses.

The Institute for Fiscal Studies economic think tank has suggested the poorest households might be facing inflation of 10.9%.

This is higher than average because they spend a larger portion of their money on heating and lighting their homes.

A Treasury source pointed to previous comments made by Mr Sunak in which he said he was “ready to do more” and that he was “learning more” about what was going on in the economy every week.