Prime Minister David Cameron today said the shooting of WPC Yvonne Fletcher was 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.
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 Transitional National Council (TNC) 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 said last night that 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 claim 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 TNC to extradite Matouk for a trial in the UK.
He said: "We want to do everything we can to make sure that the friends and the family of Yvonne Fletcher - who, of course, have been mourning for years and years and years, but must feel their loss even more sharply given recent events - are given answers and that the people who were responsible for that killing are brought to justice.
"Of course, we'll be looking to the new Libyan administration to help us in that."
Mr Cameron will travel to Paris for an international conference on Libya tomorrow aimed at providing support to the TNC.
Meanwhile, a senior MP has said claims that one of Gaddafi's sons attempted to negotiate his surrender to rebel authorities in Libya are a sign the "wheels are really coming off" the dictator's regime.
The rebel commander in Tripoli, Abdel Hakim Belhaj, said Saadi Gaddafi rang him to discuss giving himself up.
Sir Menzies Campbell, a member of the Commons Foreign Affairs Select Committee, said it was a sign the despot's regime was crumbling and called on Col Gaddafi to "accept the inevitable" and surrender.
Mr Belhaj said Saadi first called him on Tuesday and asked whether his safety could be guaranteed.
He said: "We told him 'Don't fear for your life. We will guarantee your rights as a human being and will deal with you humanely'."
The claims have not been confirmed but former Liberal Democrat leader Sir Menzies said: "If these reports are true, then the wheels are really coming off the Gaddafi camp.
"A great deal of bloodshed could be avoided if Col Gaddafi himself would accept the inevitable."