Luke Coffey said the prime minister had used the pledge to convince Dr Fox, then the defence secretary, and senior military personnel to sign up to the initial round of cuts to the Ministry of Defence’s budget in 2010.
He told the Today programme: “It was very clear to Liam Fox and his ministers, Jock Stirrup and his service chiefs that there would be a real-terms increase in the defence budget between the years 2015 and 2020 – that’s what made this difficult pill to swallow that much easier.”
Coffey, who now works at the Heritage Foundation think-tank, also said that there were threats of resignations “en masse” in the military leadership over the government’s initial proposals.
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“There was certainly concern that if the defence cuts that were first talked about to the Ministry of Defence actually took place, that was a real possibility.”
The Conservative leadership is coming under pressure to make a manifesto commitment to spend at least 2% of GDP on defence through the next parliament, as some forecasts suggest it will fall beneath the Nato target level within two years.
Fox is one of a number of Conservative backbenchers to back the target, while the US and senior former defence bosses have also expressed concern.
The Financial Times reports today that Cameron has asked ministers to check whether the intelligence agency budget can be counted as defence spending, in a bid to meet the 2% target.
The paper says the Prime Minister wants to "pad out" the defence budget in order to head off criticism by the United States that Britain's military spending is too low.