Jeremy Hunt will promise to increase spending on defence by a quarter during the next five years, as he seeks to woo the grassroots Tories who will select Britain’s next prime minister.

The foreign secretary is the underdog in the race to succeed Theresa May, with Boris Johnson the clear favourite, but the defence pledge is the latest of a series of policy announcements aimed at enthusing the Tory grassroots – and highlighting the lack of clear policies in Johnson’s leadership platform.

Hunt will say on Tuesday: “I was the person who secured a historic funding boost for the NHS and as prime minister I’ll do the same for defence. Everyone knows Britain is a world-leading soft power but, to be credible, we need to show that we are determined to remain a first-rank military power.

“My plan for defence will give our brave troops the backing they need and show the world that, when it comes to the new threats to western values, Britain is back and Britain’s voice will be strong.”

Hunt’s plan would be expected to increase defence spending by £15bn by 2023-24. That would use up more than half of the £27bn of fiscal headroom set aside by the chancellor, Philip Hammond, who told MPs in his spring statement that it would be possible to ease austerity, but only if the government could avoid a no-deal Brexit.

Hammond told all the Conservative leadership candidates to avoid making unfunded spending promises during the campaign to avoid squandering the Tories’ reputation for managing the public finances.

The chancellor said earlier this month: “We have over a long period built the hard-won reputation for fiscal responsibility and managing the economy and the public finances and I want to ensure that the candidates commit to carrying on with the work that we’ve been doing over the last nine years.”

Johnson used his Telegraph column to set out plans for increasing the higher-rate income tax threshold from £50,000 to £80,000, a generous tax cut that would go entirely to higher earners.

All the leadership candidates – who have now been narrowed down to just Hunt and Johnson – made spending promises, on everything from education to social care.

The defence secretary, Penny Mordaunt, praising Hunt’s promise of what his campaign called a “war chest”, said: “The first duty of any prime minister and any government is to protect the United Kingdom and further her interests. The British public want us to have clout in the world. We must give the men and women of our armed forces what they need to do the job we ask of them.”