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It has emerged that Ms Burton watched BBC television reports of her “release” while she was still in captivity.
British officials have already spoken briefly to Ms Burton, 24, and her parents after their release but are keen to find out more. However, Ms Burton was extremely reluctant to give any descriptions of her captors.
“Kate had long ideological discussions with the kidnappers which certainly tired her out,” one official said, “but we have been trying to impress on her that it was serious and that she was kidnapped.”
The two specialist hostage negotiators who flew out from Britain were closely involved in the tense behind-the-scenes talks that went on for 18 hours with the previously unknown Palestinian militant group who seized Ms Burton, her father, Hugh, 73, and mother, Win, 55.
Yesterday Ms Burton was in the West Bank city of Ramallah; but she said that she intended to continue her aid work with the Palestinians after her parents flew home to Brussels late on Saturday.
Although the kidnapping was denounced by many Palestinian groups, masked gunmen yesterday seized an Italian peace activist, part of a group that included two MEPs, in the southern Gaza town of Khan Younis. He was freed by Palestinian security forces four hours later after a gun battle.
In another sign of Gaza’s deteriorating security situation, which saw the end of a year-long truce, militants stormed a UN club which was empty at the time. Ms Burton, who speaks Arabic, told colleagues and friends that she hoped to return to Gaza next week and continue her job with the al-Mezan human rights group, where she has worked for three months.
Details of the efforts to free Ms Burton and her parents are still shrouded in secrecy, but it emerged that the family were moved three times during their ordeal. They were held at a house in Rafah, where they were seized, another in nearby Khan Younis and finally in Gaza City before being handed over to British diplomats.
Their moment of freedom was delayed by six hours as the previously unknown group, the Brigades of the Mujahidin, demanded that a video tape be aired as a condition for the release. Ms Burton is seen standing passively while an armed, masked gunman reads a statement threatening further kidnappings and demands that Britain intervene with Israel on behalf of the Palestinians.
However, a power blackout had slowed the process as the militant group, now believed by British security officials to be a splinter of the Popular Resistance Committees, could not edit the video.
Last night Seren Wildwood, 47, Kate Burton’s half-sister, said that she had spoken to her father, Hugh.
“I am extraordinarily relieved. I spoke to him briefly after he was released. He was playing it down like it was an interesting adventure in an extraordinary holiday.
Mrs Wildwood added: “I had never thought that anything like this could happen to Kate. We accepted that there was a risk. We had never deterred her from being in Gaza.
“It’s been reported that she badgered her kidnappers and I could believe that. You can just imagine: there’s this outcry over the kidnapping and she’s arguing with them in Arabic about ideology. They probably thought ‘get her out of here’.”
Even as the family was driven to the drop-off point at a Gaza hotel in the early hours of Saturday, Mr Burton feared that he was being kidnapped a second time. The kidnappers’ car was shadowed by under- cover Palestinian security forces, and when it came to a halt Mr Burton bolted for freedom, only to be tackled by a British diplomat who bundled him into another vehicle.
Two other British officials convinced Ms Burton and her mother that they were there to help and they got into another car that whisked them out of Gaza and back to Jerusalem.
The Foreign Office has denied that any ransom was paid.
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