Foreign secretary William Hague has said the Libyan regime is "crumbling from within" following the defection of Libyan foreign minister Moussa Koussa.
In what diplomatic correspondent James Robbins described as "a significant contact", a Libyan government envoy, Mohammed Ismail, has been in London in the past few days for talks with the British authorities.
World affairs editor John Simpson said it was "not unlikely" that the Gaddafi regime was "seeing what the situation is" concerning an exit from power.
But the defection and diplomatic developments pose a moral and legal dilemma for the UK.
Human rights lawyer Geoffrey Robertson QC told the programme that "the days in which dictators used to exit the bloody stage with the amnesty in the back pocket and the Swiss bank account intact are long gone."
But former solicitor general Vera Baird said that the priority with defectors was to "try and save Libyan lives now" although they would nevertheless have to face "ultimate culpability".
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