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MPs are due to debate the options for restoring the building - including a total evacuation of MPs and peers while work is carried out - in the coming months, although there will be no vote for about 18 months.
Mr Leakey, who was in charge of controlling access to and maintaining order within the House of Lords, told Radio 4's Westminster Hour there was no excuse for Parliament not to take every available precaution given the age of the building and the antiquated nature of its wiring and stonework.
A live fire drill while the Commons and Lords were sitting had been recommended, he said, and was "very likely" to happen - irrespective of the inevitable disruption it would cause.
A controversial proposal for MPs and peers to vacate the traditional home of parliament is the subject of a free vote in the Commons this week.
Margaret and Simon Barrett says...