The Libyan government is assisting detectives investigating the murder of Pc Yvonne Fletcher more than 20 years ago, Scotland Yard has said.
Yvonne Fletcher was killed at a demonstration in 1984
Commissioner Sir Ian Blair said a team of investigators had travelled to Libya and authorities were "co-operating".
Pc Fletcher, 25, was shot while policing a protest outside the Libyan embassy in London in April 1984.
Prime Minister Tony Blair met the country's leader Colonel Muammar Gaddafi this week for talks.
Sir Ian revealed the investigation's development at a meeting of the Metropolitan Police Authority.
He said officers had visited the north African country, but added: "It would not be correct to say we have identified the person responsible yet."
A joint investigation between British and Libyan police into the murder was launched in 2004.
It followed talks between Mr Blair and Mr Gaddafi after Britain and the US had persuaded the state to give up ambitions on nuclear weapons.
Pc Fletcher, originally from Semley, near Shaftesbury, was shot dead as, together with other officers, she policed a demonstration against Mr Gaddafi's regime outside the Libyan People's Bureau in St James's Square on April 17, 1984.
The bullet which killed her was fired from inside the embassy and Scotland Yard has long suspected that Libya knows the identity of the man who fired it.
But the killer is thought to have been smuggled out of Britain after the shooting, claiming diplomatic immunity.
Eleven demonstrators were also injured.
On Tuesday Mr Blair praised "positive" talks with the Libyan leader on issues such as defence, counter-terrorism and business.
He said relations had been "completely transformed" since ties with Tripoli were broken off in 1994.
Diplomatic relations were restored in 1999 after the country accepted "general responsibility" for Pc Fletcher's murder and agreed to pay compensation to her family.