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.

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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.

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