The dramatic details of how the SAS completed a "brilliant" rescue of a British aid worker and three other female hostages in Afghanistan can be revealed.
Defence sources said the "surgical" operation showed the "precision, skill and courage" of British special forces after they stormed the cave where Helen Johnston, 28, was held, and killed her kidnappers.
David Cameron spoke individually to the soldiers to thank them for an "extraordinarily brave" mission. He warned that anyone who took British citizens hostage faced "a swift and brutal end".
Miss Johnston, a committed Christian, along with Moragwa Oirere, a Kenyan colleague, and two Afghan women who worked for the same aid agency, were said to be physically well after their ordeal.
Miss Johnston's parents expressed their gratitude to the SAS and American Navy Seals from the same unit that killed Osama bin Laden, for freeing their daughter. Mr Cameron spoke to the rescued aid worker as she recovered at the British embassy in Kabul.
The raid was ordered by commanders amid mounting fears that Miss Johnston and the other three captives, who were seized on May 22, were in danger of being killed or handed over to more dangerous terrorists.
On Saturday night, sources said it had been a "classic operation" that was "brilliantly executed" after days of painstaking intelligence gathering. The hostages' exact location was pinpointed early last week using mobile phone interception technology. Predator drones flying silently at 20,000ft kept their captors under 24-hour surveillance.
International Security and Assistance Force (ISAF) commanders hoped initially that the kidnapping would be resolved peacefully. Shortly after the four women were seized, the kidnappers, who were known to have close links to the Taliban, released a video in which they demanded a £6 million ransom and the release of a comrade.
But by Wednesday analysts had received intelligence that the hostages had been spilt into two groups and were being held in separate caves in a forest in a mountainous valley in Badakhshan, north-east Afghanistan.
Concern for the women's safety increased when a member of the Taliban was overheard in an intercepted mobile phone conversation pressurising the kidnappers to put on a "show of intent".
Mr Cameron was informed on Friday by General John Allen, the US Commander of ISAF in Afghanistan, that the time had come for a military response to the emergency. The Prime Minister gave his approval before briefing members of Cobra, the Government's emergency committee, on Friday afternoon.
The plan went into action almost straight away. The team of around 70 special forces troops were already at a forward operating base in Badakhshan province, with a fleet of Black Hawk helicopters and Apache gunship escorts.
This was an operation in very demanding terrain, high mountains and deep gullies, and very arid and demanding. It was carried out by immensely professional troops who applied precision, skill, and courage
They flew to a pre-arranged rendezvous in a high mountain valley around two miles from where the hostages were being held and marched two miles through thick forest, moving into assault positions around the caves.
In Kabul, Gen Allen and his British deputy, Lieutenant General Adrian Bradshaw, watched screens showing footage of the assault from a Predator drone and head cameras worn by the soldiers, so that they could maintain "full operational awareness".
Around 7pm local time the US and British troops stormed the two caves, killing 11 kidnappers within minutes. There was a moment of alarm when the US troops reported back that although they had shot dead seven kidnappers, the cave they assaulted did not contain any hostages. The tension was broken, however, when the SAS commander on the ground reported that his team has successfully rescued all four hostages.
A military source said: "This was a classic operation. All the bases were covered and it was executed brilliantly. The strike was made with surgical precision - we were 95 per cent sure of the kidnappers' exact location, weapons and motives. The SAS and the US special forces were always ahead of the game once the kidnappers' position had been fixed."
Lt Gen Bradshaw said: "This was an operation in very demanding terrain, high mountains and deep gullies, and very arid and demanding. It was carried out by immensely professional troops who applied precision, skill, and courage."
In Downing Street yesterday, Mr Cameron said: "It was an extraordinarily brave, breathtaking even, operation that our troops had to carry out. I pay tribute to their skill and dedication."
Miss Johnston, who completed an MSc in nutrition at the London School of Hygiene and Tropical Medicine, had been working in Afghanistan with the international aid charity Medair for a little over a year. In a newspaper interview in November, she said: "Some of things I have seen I have had a very emotional reaction to. The children come to the clinic draped in clothes, looking quite big, but then you roll up their sleeve to measure them and you see their tiny little frames. They look other-worldly."
Her father Philip, a theologian and senior tutor at Hughes Hall at Cambridge University, and mother Patricia said in a statement: "We are delighted and hugely relieved by the wonderful news that Helen and all her colleagues have been freed.
"We are deeply grateful to everyone involved in her rescue, to those who worked tirelessly on her behalf, and to family and friends for their love, prayers and support over the last 12 days."
The Sunday Telegraph, London