In a diplomatic breakthrough, the Foreign Secretary, Robin Cook, told the Commons that the offer by Colonel Muammar Gaddafi "fully meets" the objectives of successive British governments since the murder. Mr Cook said the move was supported by PC Fletcher's family and the Metropolitan Police.
He said the breakthrough would lead to the British Interests Section in Tripoli being upgraded to full embassy status and an ambassador appointed "as quickly as practical".
A joint statement following weeks of negotiation between Britain and Libya stated that Libya would co-operate with a Metropolitan Police investigation into the killing.
Yvonne Fletcher, 25, was shot outside the Libyan People's Bureau in St James' Square, central London, while policing a demonstration. It was suspected that she died from a bullet from a burst of machine-gun fire from within the building, but Libya refused to co-operate with the police and the murder led to diplomatic relations being broken off.
The 22 Libyan embassy officials were allowed to leave the building 10 days after the shooting and flew back to Tripoli.
Following Colonel Gaddafi's offer yesterday, the Fletcher family said in a statement: "We have waited a long time for Libya to acknowledge its responsibility for the actions of those in the Libyan People's Bureau on April 17 1984."
It went on: "No one can any longer cast doubt on what has happened. We hope that there can now be progress on identifying precisely who was responsible for Yvonne's death. The path to full justice for Yvonne is now open."
During the last three months, Libya's ambassador to Rome, Abdul-Ati al-Obeidi, has held four meetings with a Foreign Office official to reconcile the Fletcher issue. A statement was finally agreed at a meeting between Mr Obeidi and Mr Cook yesterday afternoon.
The Foreign Secretary told Parliament: "In that statement, Libya accepts general responsibility for the actions of those in the Libyan People's Bureau at the time of the shooting.
"They express deep regret to the family of WPC Fletcher for what occurred and offer to pay compensation now to the family. Libya agrees `to participate in, and cooperate with, the continuing police investigation and to accept its outcome'."
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