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Thatcher expressed her support in a vote in the House of Lords (Monday) on a motion by former foreign affairs minister Lord Chalfont for a select committee to investigate the decision to blame two pilots for the crash of ZD576.
The motion, which follows a long campaign by Computer Weekly, was opposed by 106 peers.
All four crew and 25 senior police and intelligence personnel died in the crash. The report of an RAF Board of Inquiry found that problems with the helicopter's troubled computerised Full Authority Digital Engine Control (Fadec) system could have contributed to the crash. However, the inconclusive findings of the report were overturned by two air marshals, who oversaw the outcome of the formal investigation into the crash.
There was drama in the Lords debate as some peers said that a vote for a select committee to reopen the investigation would be unprecedented. "This is an unusual constitutional matter," said Lord Tordoff, chairman of the House of Lords Liaison committee.
Peers who were against the select committee said it was wrong for the House of Lords to put the two air marshals in the dock.
But Lord Ackner, a former Law Lord, said there were doubts over the cause of the crash and under RAF rules deceased aircrew could be found negligent only if there was no doubt whatsoever.
Speaking after the vote Chalfont said; "I had support from all sides of the House. Mrs Thatcher supported and congratulated me on the result. She is really on our side."
Lord Chalfont's original motion proposed that the Lords set up a select committee to investigate all the circumstances surrounding the crash. This would have included a review of claims by the Public Accounts Committee and Computer Weekly that Parliament had been misled on technical matters related to the crash and the investigation.
Now the select committee's review will be limited to a review of the findings against the pilots of ZD576.
Defence Minister Baroness Symons said she welcomed Lord Chalfont's "compromise" motion.
However, critics have warned that the dilution of the original motion may leave the door open for the liaison committee to block a full Lords inquiry.