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The aircraft was thought to have come down due to a technical fault at 13.30pmBST (4.30pm local time) 12 miles west of Kandahar in southern Afghanistan.
A spokesman for the International Security Assistance Force (ISAF) said enemy action had been discounted at this stage.
An MoD spokesman said: "The Ministry of Defence is extremely sorry to have to confirm that the aircraft lost in Afghanistan earlier today supporting an ISAF mission was British, and that the crash led to 14 fatalities, 12 RAF, a Royal Marine and one from the Army."
Defence Secretary Des Browne described the news of the deaths as "dreadful and shocking" and said it appeared to have been a "terrible accident".
He said: "I know that the people of Britain will join me in sending our deep condolences to the loved ones of those who have lost their lives, and to the British military as it deals with the loss of friends and comrades.
"This is not the time for speculation, as the operation to secure the crash site is ongoing. We will provide further information as soon as there is more to say.
"Everyone will understand that our first priority is to inform and support the families of those on board.
"I can say, however, at this stage all the indications are that this was a terrible accident and not the result of hostile action.
"This tragic incident should serve to remind us all of the risks the British military shoulder on all our behalf, across the world every day."
The MoD has set up a helpline for worried relatives on 08457 800 900.
No details have yet been released of the type of aircraft involved.
Today's crash is thought to be the biggest single loss of British troops in Iraq or Afghanistan since the war on terror began in November 2001.
Ten British armed personnel were killed when a Hercules C130K crashed 19 miles north-west of Baghdad on January 30, 2005.
News of today's crash emerged shortly after 2pm today when ISAF reported an aircraft "missing" in southern Afghanistan.
ISAF spokesman Major Luke Knittig said the aircraft had made an emergency call shortly before it disappeared.
Locals near the scene described how coalition force helicopters were seen flying towards the crash site.
Haji Eisamuddin, a local tribal elder, said the wreckage of the plane was burning in an open field.
"I can see three to four helicopters in the sky, and coalition forces are also arriving in the area," he said.
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