The plane was a Nimrod MR2
Twelve RAF personnel, a Royal Marine and an Army soldier were on board the RAF Nimrod MR2 which came down in the southern province of Kandahar.
The reconnaissance plane, based at RAF Kinloss in Scotland, belonged to the Nato-led force battling the Taleban.
Officials said the incident appeared to be an accident and Tony Blair said it would "distress the whole country".
The prime minister said: "Our thoughts go out immediately to the families of those who have died.
"British forces are engaged in a vital mission in Afghanistan and this terrible event starkly reminds us of the risk that they face daily."
The 12 RAF personnel on board the plane were all based at Kinloss and from the Moray area, a spokesman from the base said.
All next of kin have been informed.
UK Defence Secretary Des Browne described the incident as "dreadful and shocking" news and said the indications were it was a "terrible accident".
He added that "people needed to understand" why UK forces were in Afghanistan.
"We are there in the context of a UN resolution - at the request of the United Nations Nato has taken on this very difficult task," he said.
"The developed world can't afford to allow Afghanistan to become a training ground for terrorists again.
"The whole of the developed world knows that and that's why almost all of the developed world - the whole of the civilised world - has troops and others present working with us on this task."
Angus Robertson, the SNP MP for Moray, said: "This is tragic news for the families and friends of the service personnel at RAF Kinloss.
"It brings home the terrible danger that our service personnel face and that they perform their duties with selflessness.
"Our thoughts go out to everybody connected with the victims and RAF Kinloss at this time."
'Technical fault'
Nato forces say the plane was supporting the Nato mission in the area.
The pilot is believed to have radioed ground staff about a technical fault shortly before the aircraft came down.
The crash brings the death toll of UK forces personnel in Afghanistan to 36 since the start of operations in November 2001.
Defence analyst, Major Charles Heyman, told BBC News 24: "It's a black day. It's a disaster for our soldiers on the ground in Afghanistan.
"No other words can describe it. It's a big hit to morale. Believe me it really does affect morale."
Commander of British Forces in Afghanistan, Brigadier Ed Butler, said recent loss of life has caused "profound personal devastation for families, friends and colleagues".
But he paid tribute to the "quite remarkable" resilience and morale of British service personnel.
"I am personally humbled by their courage and commitment in getting on with the tough job in hand; delivering over and above, and making a difference to the ordinary people of Afghanistan," he said.
BBC defence correspondent, Paul Wood, told BBC News 24, said the plane could have been supporting an operation in a place called Panjwayi - west of Kandahar.
"It's a town - which has been in Taleban hands - which has been forced back into coalition hands by a big push, still continuing today."
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Conservative Party leader David Cameron, who said he was "deeply shocked and saddened" by the accident, has sent his condolences to the friends and families of those killed.
"Today's tragic loss is a reminder of the extraordinarily difficult conditions in which our armed forces are operating in Afghanistan," he said.
Afghanistan is experiencing its bloodiest period since the fall of the Taleban in 2001, with much of the fighting concentrated in the south.
There are 5,500 British troops in the country, helping to train Afghan security forces, facilitate reconstruction, and provide security.
But in Helmand, the emphasis is also on counter-narcotics, as the province is the "largest single source of opium in Afghanistan".
British troops have found themselves in virtually daily gun battles with the Taleban, who have been regrouping.
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The crash comes as Afghan and Nato troops began a major anti-Taleban drive in the Panjwayi district of Kandahar.
The plane came down about 20 km (12 miles) west of the city of Kandahar, Maj Scott Lundy of the International Security Assistance Force (Isaf) said.
There was no indication of an enemy attack on the plane, which was not a fighter jet.
It was "supporting a Nato mission. It went off the radar and crashed in an open area", he said.
The crash is thought to be the biggest single loss of British troops in Iraq or Afghanistan since military operations began there in 2001.
Ten British armed personnel were killed when a Hercules C130K crashed north-west of Baghdad in January 2005.
There have been four previous crashes of Nimrods since 1980, two of them involving fatalities.
The last took place 11 years ago to the day when seven crew from Kinloss died at an air show near Toronto, Canada.
The incident was blamed on pilot error.
Un avión de la OTAN se estrelló este sábado en el sur de Afganistán, causando la muerte de 14 soldados británicos. Según la OTAN nada indica que el avión haya sido derribado.

El accidente sucede después de un día de combates en el sur del país, donde 9 policías afganos, 13 insurgentes talibanes y un soldado británico perdieron la vida.

Según el mayor Scout Lundy, vocero de la Fuerza de Asistencia de Seguridad Internacional de la OTAN, el aparato brindaba apoyo a la misión de la OTAN cuando desapareció del radar un área de la provincia de Kandahar, cerca de 20 kilómetros al occidente de la ciudad homónima.

Lundy dijo que no había ninguna indicación de un ataque enemigo, sino que la tripulación del avión reportó problemas técnicos antes de caer.

Sin embargo, inmediatamente después del accidente un vocero del Talibán, Abdul Khaliq, se atribuyó la responsabilidad del incidente: "usamos un misil Stinger para derribar el aparato", afirmó.