A Libyan man arrested on suspicion of conspiracy to murder PC Yvonne Fletcher has been released on bail.
PC Fletcher, 25, died after being shot while policing a demonstration outside the Libyan Embassy in London in 1984.
The man, in his 50s, was arrested on Thursday by counter-terrorism officers in south-east England. He was also held on suspicion of money laundering.
Two other Libyan nationals - a woman in her 40s and a man in his 30s - were also held and later bailed.
They were arrested on suspicion of money laundering at separate addresses in London and south-east England.
PC Fletcher's family said in a statement on Thursday that her father Tim had recently died, with his "one regret in life" being that he had "never witnessed any justice".
The Met is offering a reward of up to £50,000 for information.
PC Fletcher was one of 50 officers policing a protest against Col Muammar Gaddafi's regime outside the embassy in April 1984 when she was hit by a burst of gunfire from a first-floor window.
The death of Gaddafi in 2011 and the subsequent regime change provided new lines of enquiry, with police visits to Libya since then unearthing "new and fresh evidence".
The force has released images of 14 people officers want to trace from a pro-Gaddafi group, which was holding a counter-demonstration nearby.
Video footage of the demonstration and shooting has also been released, showing the chaotic moments after shots were fired.
The shooting of PC Fletcher sparked an 11-day siege of the Libyan embassy and diplomatic ties between Libya and the UK were severed following the killing.
Timeline of events and developments in the investigation
- 17 April 1984: PC Fletcher is killed while policing a demonstration outside the Libyan embassy in central London. An 11-day siege begins and diplomatic links with Libya are brought to an immediate end. When the siege ends all Libyan diplomats make their way out of the embassy and are given diplomatic immunity.
- 7 July 1999: The Libyan government accepts "general responsibility" for the shooting of PC Fletcher and offers to pay compensation to her family. The next day, Scotland Yard announces it is to reopen the investigation into PC Fletcher's death.
- 2 May 2002: Scotland Yard officers fly to Libya as part of the investigation into PC Fletcher's death but return with no real leads to follow.
- 25 March 2004: Tony Blair meets Colonel Gaddafi in Libya for talks, and the then foreign secretary Jack Straw announces that Met police officers will fly there on 3 April 2004, in a fresh attempt to find PC Fletcher's killer.
- 14 September 2009: Details are released on a deal between the British and Libyan governments in 2006, agreeing that any murder suspects will be tried in Libya. PC Fletcher's family say they knew about the deal and "feel in no way misled" by it.
- 11 May 2012: Two Met counter-terrorism detectives travel to Libya, to continue investigations.
- 3 January 2014: Papers on the killing, released under the 30-year rule by the National Archives, reveal that the day before the killing Libyan officials were warned three times about potential violence if the demonstration went ahead.
- 19 November 2015: Scotland Yard says a Libyan man in his 50s is arrested on suspicion of conspiracy to murder PC Fletcher. Police offer a reward of up to £50,000 for information about the killing. He is subsequently given bail.