Chief of the Defence Staff General Sir Nicholas Houghton also said he would "worry" if someone with Mr Corbyn's views on Trident became Prime Minister. 

The Labour leader believes the general has breached constitutional principles because top military staff are expected to remain neutral on key political issues.

Sir Nicholas said not taking part in Syria airstrikes was like being asked to win a football match without going into the opponents' half.

He argued it "makes no sense" given the territory held by IS spanned the border with Iraq, and that its powerbase is in Syria.

"The source of their power, their command and control, their logistics, their organisation, the place from which they issue orders to international terrorists is from within Syria.

"And so to be denied our ability to play a proportionate role in that makes no sense."

In a separate BBC interview with Andrew Marr, the Chief of the Defence Staff said Mr Corbyn's refusal to press the nuclear button under any circumstances would "seriously undermine" the credibility of the Trident deterrent.

The Labour leader hit back swiftly, describing the remarks as "unhelpful" – and said he would be writing to Defence Secretary Michael Fallon to request "the neutrality of the Armed Forces is upheld".

In a statement, the Leader of the Opposition added: "It is essential in a democracy that the military remains politically neutral at all times.

"By publicly taking sides in current political arguments, Sir Nicholas Houghton has clearly breached that constitutional principle."

This is not the first time Mr Corbyn has clashed with the military.

Shortly after he won the Labour leadership election in September, an unnamed serving general told The Sunday Times there would be "mutiny" if the left-wing leader became Prime Minister in 2020.

His intervention comes after Michael Fallon said the case for Britain's involvement in Syrian airstrikes would be strengthened if IS militants were found to be responsible for downing the Russian passenger jet in Egypt.

The Defence Secretary argued it was "morally indefensible" that the UK was not currently attacking the extremist group's key strongholds.

He also denied the Government had given up on winning parliamentary backing to extend RAF action from Iraq.

David Cameron has made no secret of his desire to carry out airstrikes against IS targets in Syria.

But his ambitions suffered a setback after a report by the Commons Foreign Affairs Select Committee warned against involvement until there was an international plan to end the conflict.

Britain has already carried out strikes against IS in Iraq, but Mr Cameron will be keen to avoid a repeat of 2013 when he failed to get MPs to back action in Syria after evidence President Assad's had used chemical weapons.