Britain’s leading tax and spending thinktank has said that Jeremy Hunt’s promise to reduce corporation tax to the lowest rates in the advanced world would cost £13bn a year and risk the continuation of austerity.

The Institute for Fiscal Studies warned that the Conservative leadership contender’s plans would leave no scope to relax the Tories’ policy of austerity after a decade of cuts to public services, unless other taxes were raised or the public debt was increased.

Paul Johnson, director of the IFS, said cutting corporation tax and another promise made by Hunt to raise defence spending would “leave no scope to relieve the pressure on other areas of public spending without tax rises, or a fiscal stance which risked putting debt on a rising path”.

Lagging behind his rival, Boris Johnson, in the polls to become prime minister, the foreign secretary has proposed reducing the rate of corporation tax paid by firms to 12.5%, matching the rate in Ireland among the lowest of any major economy.

The IFS said that such a step would cost £13bn a year in the short run. While it said there was uncertainty over how much it would cost in the long-run, it disputed the claims of some low-tax advocates that the policy would pay for itself by driving up company investment and encouraging overseas firms to locate in Britain.

Sajid Javid, the home secretary, had made such an argument in the Tory leadership race before he was eliminated, saying tax cuts would raise the level of dynamism in the economy and generate greater revenue for the exchequer.

“One thing we can be fairly sure of is that a cut of this magnitude would not pay for itself,” the IFS said. “It is implausible to believe that profits earned or recorded in the UK could increase by enough to make up for the immediate £13bn fall in revenue.”

Among other policy proposals outlined by Hunt in the leadership race include plans to raise defence spending, which the IFS said would come with a hefty price tag and could detract from increased spending on the welfare state.

Profile Jeremy Hunt's Tory leadership campaign Show Hide Personal style His style is notably technocratic, with few rhetorical flourishes and an emphasis on his consensual approach and long record as a minister, notably during more than five years as health secretary, a traditional graveyard of ministerial careers. Hunt’s attempts to talk up a backstory as an 'underestimated' entrepreneur can fall flat given he is also the son of an admiral and was head boy at Charterhouse. Overall, Hunt’s approach can seem uninspiring and hard to pin down in terms of core beliefs, hence the 'Theresa in trousers' nickname among some Tory MPs. Hunt has made headlines by promising to repeal the ban on fox hunting, while always facing scrutiny on his views on the availability of abortion. His campaign team have decided to take the fight directly to rival Boris Johnson though, with Hunt taking part in a Twitter Q&A session as a direct response to Johnson's refusal to appear on a Sky TV head-to-head debate. The hashtag: #BoJoNoShow. Brexit He says a new deal with the EU is possible by 31 October and he would send a cross-party negotiating team to Brussels, including members of the DUP. He would countenance leaving the EU without a deal but is notably more wary than rival Boris Johnson. Taxation Has been fairly silent on this, beyond a proposal to cut corporation tax from 19% to 12.5%, which according to the IFS would cost an estimated £13bn a year. Even at 19%, the UK rate is well below European and global averages. Public spending Before the campaign began he called for a doubling of defence spending, but he has since pulled back slightly, saying only that it should increase. He has argued that cuts to social care budgets had gone too far. Climate and environment Hunt backs the 2050 target for zero net carbon emissions and has called for 'sensible tax incentives' to encourage green initiatives, but very little beyond this. Foreign policy A likely strength for him, as he has been seen as a solid foreign secretary, an impression burnished by taking over from the chaotic Johnson. This has been a key part of his pitch. Peter Walker Political correspondent Photograph: Luke Dray/Getty Images Europe

Potentially representing the reversal of a 70-year trend underway since the dawn of the welfare state, Hunt has proposed to raise state spending on defence as a proportion of GDP to 2.5% from the current level of 2%. He had previously suggested the UK needed to double defence spending to 4% over a decade.

UK defence spending has gradually fallen from a high of 7% in the 1950s. Britain is one of only seven Nato countries out of 29 members to meet a target to spend 2% of GDP on defence, with most, including Canada and Germany, spending much less.

The IFS said raising defence spending to 2.5% of national income over the next five years would cost £15bn a year more in 2023−24 than today. Doubling spending over the next decade would cost more than £40bn a year.

A spokesman for Hunt said: “All of Jeremy’s pledges on more defence spending and tax cuts to turbocharge growth will be affordable as we will stick to our fiscal rule to keep debt falling relative to GDP over the cycle.

“Our policies will attract even more international investment and ensure that we keep Britain safe and walk tall in the world.”