The UK will have to significantly increase defence spending if it is to maintain influence with Washington and Nato allies, MPs have warned.

A Commons Defence Committee report says the defence budget should rise from 2% of GDP (£40bn) to 3% (£60bn).

Defence Secretary Gavin Williamson has reportedly demanded an extra £20bn for his department – but another minister warned against “unsustainable” rises. The government said it would “continue to exceed” Nato’s 2% spending target.

The committee said the extra money for the Ministry of Defence (MoD) could be spent on increasing the readiness of the armed forces and to bolster Britain’s anti-submarine warfare to counter possible threats from Russia.

The report recommends increasing the defence budget to 3% of GDP, but says a rise to 2.5% would “comfortably fill the ‘black hole’ in the existing MoD budget”. It argued that without such investment the UK armed forces’ usefulness to the US would be diminished. “The government must not let this happen,” the report says.

Defence correspondent Jonathan Beale says the committee’s report will “add fuel to what seems to be an increasingly acrimonious row between the defence secretary, Gavin Williamson, and the Treasury and the prime minister”. He says there have been warnings of a Conservative backbench rebellion if more funding is not forthcoming.

Over the weekend the Mail on Sunday reported that Mr Williamson threatened to end Theresa May’s leadership if she did not provide more money. But Chief Secretary to the Treasury Liz Truss warned cabinet colleagues that it is “not macho” to demand more funding.

Writing in the Daily Telegraph, she said: “It’s much tougher – and fairer to people – to demand better value for money.” Increasing taxes to fund extra spending would “hamper the success of post-Brexit Britain”, she added.

Lord Houghton, who was the chief of defence staff between 2013 and 2016, said “it would be a great shame” if the armed forces budget was used as part of a “political game”. He told BBC Radio 4’s Today the current defence plans were “unaffordable” and the UK needed to “make a decision” about “what sort of country we aspire to be”.

Lord Houghton said: “The first duty of government is the protection of the nation. “We have slightly deluded the public of late that we have a defence programme that frankly we know is unaffordable. “We are to an extent living a lie.”

The MPs’ report also notes comments by US Defence Secretary James Mattis that the UK benefits from its defence relationship with the US by £3bn a year. “This implies that both the UK armed forces and HM Treasury benefit from our close relationship with the US,” the report says. “However, that will continue to be true only while the UK military retains both the capacity and capability to maintain interoperability with the US military and to relieve US burdens.”

At next month’s Nato summit in Brussels, US President Donald Trump is expected to repeat his demands for European allies to spend more on defence.

Defence committee member Madeleine Moon, Labour MP for Bridgend, said the UK’s armed forces have been “hollowed out” with the navy “very weak” and air capability “diminished”. She told Today: “Influence is really important because unless you can back it up with capability, you have no credibility.”