Prime Minister David Cameron has said the shooting of WPC Yvonne Fletcher is a reminder of the "horrors" of the Gaddafi regime and expressed hope that the rebel authorities would co-operate in the investigation into her murder.
Policemen attending to Wpc Yvonne Fletcher who was shot during demonstrations outside Libyan Embassy.
Only one of the three main suspects in the 1984 killing is believed still to be alive but Mr Cameron said he was sure that the National Transitional Council (NTC) would assist British police in their investigation.
Deputy Prime Minister Nick Clegg also said the Government will do "everything we can" to get answers for WPC Fletcher's family.
Rebel officials in Tripoli on Tuesday night said one of the suspects for WPC Fletcher's murder, Abdulqadir al-Baghdadi, had been shot in the head. He was an official at the Libyan embassy in London at the time of the murder.
Reports in the Daily Telegraph claimed that junior official Abdulmagid Salah Ameri, who was suspected of firing the fatal shots, is also thought to have died. That left Matouk Mohammed Matouk as the last named suspect believed to be still alive, it added.
Negotiations have begun so that officers from the Metropolitan Police investigating the murder of WPC Fletcher, who was gunned down while on duty at a protest against Colonel Muammar Gaddafi's regime outside the Libyan embassy in London, could travel to Libya once the security situation improves.
Mr Cameron said: "There is an ongoing police investigation and I am sure the new authorities in Libya will co-operate in that investigation."
He added: "The murder of Yvonne Fletcher was a reminder of the horrors that happened under the Gaddafi regime, and we should be celebrating today that that regime is coming to an end, and that Britain has played a proud part in that."
Mr Clegg said the Government would be "looking to the new Libyan administration to help" when he was asked if pressure would be put on the NTC to extradite Matouk for a trial in the UK.
Mr Cameron will on Thursday travel to Paris for an international conference on Libya aimed at providing support to the NTC.