Detectives from Scotland Yard's Anti-Terrorist Branch have flown to Libya to resume investigations into the murder of WPC Yvonne Fletcher.
WPC Yvonne Fletcher was shot in 1984 outside the Libyan Embassy
She was shot dead as she policed a demonstration outside the Libyan Embassy in London in 1984.
The bullet which killed her was fired from inside the Libyan People's Bureau and the Yard has long suspected it knows the identity of the man who fired it.
Plans for the Libyan trip were announced last week by Foreign Secretary Jack Straw, who claimed the Libyan authorities had been "tardy".
"It is terrible and it remains something that is a daily, hourly, nightmare for the parents concerned, to whom I have spoken," he told the BBC.
The visit to Tripoli is part of the diplomatic deal to allow the country back into the international fold.
Tony Blair welcomed Libya back into the international community
Four detectives will spend the next few days in Libya finding out who they will be able to interview and what documents they will have access to in a murder case which has left a bitter taste at Scotland Yard for 20 years.
The main suspect was among 22 Libyan officials who were allowed to leave Britain after the shooting under the cloak of diplomatic immunity.
The police would have liked his arrest to be one of the conditions of Libya's acceptance back into the international community.
But all they have got is permission for officers to return to Tripoli for a third time with no guarantee that the case will ever be successfully concluded.
Libya's failure to co-operate with the investigation into WPC Fletcher's killing was among Conservative objections to Tony Blair's recent mission to Tripoli, where he shook hands with the country's leader Colonel Gaddafi.
A Scotland Yard spokesman said he would not discuss how long the officers would stay in Libya or reveal any other details of their trip.
The Metropolitan Police Federation, which previously said relations with Libya should not resume if there is no justice for WPC Fletcher, have welcomed the move.
Chairman Glen Smyth has previously told BBC News Online it was inconceivable that the Libyans did not know who was responsible for her death.
The unsolved murder hasn't been forgotten by Scotland Yard
"It's just not acceptable that one state murders the police officers of another. It's time they came clean."
"What we would like to see is that officers can have access to the suspect and, if it transpires they can get sufficient evidence, for the Libyans to co-operate with extradition."
Despite accepting responsibility for the murder in 1999, in February the Libyan prime minister Shukri Ghanem stunned the international community when he told the BBC that his country did not accept guilt for either WPC Fletcher's death or the Lockerbie bombing.
He claimed the former issue was "settled".