Britain's commitment to the war in Afghanistan will continue under the new Government - but a battle is brewing in Whitehall about cutting defence costs.

The Conservatives' new Defence Secretary, Liam Fox, has launched an immediate strategic defence review into what form the UK's armed forces should take in the future.

He stressed his commitment to replacing the Trident nuclear deterrent, something the Liberal Democrats bitterly opposed during the General Election campaign.

There is also likely to be heated debate within the Tory-Lib Dem coalition about other costly defence equipment projects, including the Eurofighter Typhoon, the A400M military transport aircraft and plans for two new aircraft carriers.

It has long been recognised that the defence budget will be under threat as the new Government attempts to tackle the large national debt built up during the economic crisis, and former defence secretary Bob Ainsworth warned of "tough choices" ahead on military spending as he unveiled a Green Paper on the future of the armed forces in February.

Speaking outside the Ministry of Defence on Wednesday, Dr Fox said the strategic review was "the most important thing that we need to kick off". He added: "We desperately need a defence review, which is why it will begin immediately - it will begin today."

Splits between the Tories and Lib Dems over the future of submarine-borne Trident nuclear missiles were highlighted by the televised leadership debates during the election campaign, with Lib Dem leader Nick Clegg saying Labour and the Conservatives were locked in a "Cold War time warp" over the issue and argued that the future of the nuclear deterrent should be decided as part of the strategic defence review.

Dr Fox said on Wednesday: "We have got a very clear agreement that we will continue with the nuclear deterrent. I will certainly want to scrutinise the cost of the Trident replacement programme.

"But the ultimate responsibility is to keep Britain safe and protect the generations of the future from whatever threats may emerge in a dangerous world."

Afghanistan did not loom large in the election, partly because the campaign was dominated by the economy and partly because the UK death toll dropped significantly in April, but there are still about 9,500 British troops serving in the war-torn country, most of them in Helmand Province in the south, and the bloody conflict will remain the MoD's immediate focus.