Speaking after a 90-minute meeting with Libyan leader Muammar Gaddafi in the Libyan desert near Sirte, Mr Annan praised the Libyans as "serious" in wanting to settle the affair, and predicted they might do so "in the not too distant future". Robin Cook, the Foreign Secretary, took a similar line after hearing a report of the meeting from Mr Annan, proclaiming he felt "qualified optimism" about the outcome of the weekend mission.
Tripoli also indicated that a deal was possible. The Libyan Foreign Minister, Omar al-Muntassar, said following talks with Mr Annan: "I am sure that the efforts of the Secretary-General will show positive results very soon."
Even so, the failure finally to secure the handover of Abdel Basset Megrahi and Lamen Khalifa Fhimah, the two Libyan intelligence operatives accused of planting the bomb aboard Pan Am Flight 103, has been a disappointment - especially for Mr Annan who went to Libya only after an assurance he would leave with a cast iron agreement the two men would be surrendered to face justice in a court in The Hague.
Dr Jim Swire, spokesman for the British families who lost relations at Lockerbie, said he was delighted Mr Annan and Colonel Gaddafi had met, adding that , some of the Libyan complaints over the issue were justified. He continued: "The main thing is that the two men did meet because Gaddafi is busy saying he fears a trick and that he also feels that his country has been left out of negotiations about the trial, which is true, they have. What he needs, I think, is reassurance that this really is an offer of a fair trial and I can't think of anyone better than Kofi Annan to give that reassurance."
Once again, Colonel Gaddafi's mind has proved unreadable, despite Tripoli's agreement in principle to last summer's Anglo-American offer of a trial in a third country under Scottish law, and with Scottish judges.
The one ostensible sticking point now is Britain's insistence that if convicted, the suspects should serve their sentences in a Scottish jail. Despite Britain's promise of unlimited consular access for them, Libya continues to object to this condition. Yesterday, Mr Cook once again insisted there could be no compromise on the place of imprisonment.
Mr Cook said: "The crime was committed in Scotland, logically the place they should serve their sentence is Scotland. We have no objection to the United Nations or Libya sending any number of observers to make sure that the standards are humane and people are properly looked after."
The Foreign Secretary also said he hoped the trial, at a specially built courtroom, could begin on 21 December, the 10th anniversary of the bombing.
The matter could be resolved by next Sunday, after this week's meeting of Libya's General People's Congress, or parliament. According to UN sources, Mr Montasser promised Mr Annan he would ask the Congress to approve the deal during its five-day session which starts tomorrow. Dr Swire said he was still hopeful of a solution "within weeks".
Despite the setback, London and Washington are still convinced Tripoli wants to clinch a deal, and thus end the sanctions which have largely isolated Col Gadaffi's country. Optimists believe that the latest delay is merely to save the Libyan leader from the perceived humiliation of a direct personal climbdown. In fact the People's Congress always decides in accordance with his wishes.
After his face-to-face talks with Col Gaddafi, Mr Annan was typically unflappable. "I think it was a positive development," he said of the meeting. "But in all these things you have to wait for others to do what they have to do and for you to have something concrete before you can claim victory.
In Washington, the State Department spokesman, James Foley, said the United States was "disappointed" that Libya had not complied with UN Security Council resolutions. He said: "Compliance means the turnover of the two suspects for trial. It's been almost ten years since the Pan Am 103 tragedy, this has gone on too long."could begin on 21 December, the 10th anniversary of the bombing.