Officers investigating the 1984 shooting of PC Fletcher said they know who is responsible but can not prosecute because they have been blocked from using evidence in court over "national security" concerns.
The Metropolitan police said that although "enough material to identify those responsible" had been identified, it could not be presented in court.
It led to Britain severing diplomatic relations with Libya until 1999 and has always been an obstacle in ties between London and Tripoli, along with the bombing of Pan Am flight 103 over the Scottish town of Lockerbie in 1988.
The 25-year-old female officer was killed while policing what had been a small and peaceful demonstration outside the Libyan embassy in London.
Fletcher's family said that they understood the decision, but were "deeply disappointed" by the outcome.
The man, who was arrested on suspicion of conspiracy to murder, was believed to be still in the United Kingdom, said Ken Marsh, the chair of the Metropolitan Police Federation.
A spokesman for the Met said in it had "enough material to identify those responsible" for the murder of PC Fletcher outside the Libyan People's Bureau.
His arrest was described as a "significant turning point".
'Therefore, without this material and following a review of all the evidence available to prosecutors, the Crown Prosecution Service... have informed us that there is insufficient admissible evidence to charge the man'.
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'We are deeply disappointed and frustrated that a prosecution can not proceed at this time.
However, the key material has not been made available for use in court in evidential form for reasons of national security.
PC Fletcher's colleague John Murray, who cradled her in his arms as she lay dying, said yesterday: 'I am angry this information can not be made public. "We had hoped that the latest turn of events would finally lead to some closure", it added.
"Although our investigation has always remained open, cases like this do become harder to solve over time".
"Our judgment is that this concludes what was by far the best opportunity to solve this tragic case and provide a degree of closure for the victims and their families", it said.
He said the investigation "will never be closed" but added that the chances of finding further evidence is "low".
"I regret that we have not been able to deliver the justice that the victims and their families deserve".
Home Secretary Amber Rudd praised the "hard work" of investigators. Speaking to Nick Ferrari at the Police Federation Conference, he said: "Extremely disappointed, because my own personal knowledge and as commissioner we regenerated some of the investigations, I'm very disappointed".
Steve Kamlish QC, Mabrouk's lawyer, said: 'At no stage, either in interview or since, have the police produced any evidence against my client - not a shred'.
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