Barry George, 63, was convicted of the 1999 shooting dead the TV star, 37, and spent eight years in prison before his acquittal on appeal in 2008.
Speaking ahead of a Netflix documentary about the much-loved presenter’s unsolved murder, he wants police to reopen the case.
He is taking part in the series in a bid to show the public “that there’s no way I could have done this”.
Mr George was convicted by a 10-1 majority in 2001 largely because of a tiny particle of gunpowder found in his jacket pocket.
In the 2008 re-trial, that particle was found to be so small that it was inadmissible as evidence. But the Met has not reopened the investigation.
Mr George, who lived close to Miss Dando in Fulham, West London but now lives in Ireland, has Asperger’s, frontal lobe brain damage, ADHD, learning difficulties, epilepsy and is diabetic, with poor dexterity and an inability to fully look after himself.
Miss Dando was killed on her doorstep by a single shot, fired behind her left ear, which, Mr George’s defence maintained, bore all the hallmarks of a professional hit.
The original trial heard that the assailant, with his right arm, held Ms Dando and forced her to the ground. Then, with his left hand, he fired.
Mr George’s sister Michelle Bates said: “Barry is right-handed.”
Barry and Michelle, the author of Stand Against Injustice, speak in the three-part documentary series named Who Killed Jill Dando?
Despite his 2008 release, Mr George has had no compensation and he says he was followed by police around London upon his release.
Mr George and his family are still haunted by the events of 24 years ago and what they insist was a police witch-hunt.
Asked if he feels free, he said: “Not when I feel like I’m having to look over my shoulder all the time in case there are people following me or police forces potentially trying to fit me up for something else. I rise to the challenge, because if I don’t then there are many people out there who would walk over me.”
Documents submitted to a Paris court last year suggested Ms Dando may have been killed by mistake by a Russian hitman who meant to target another BBC journalist. Court papers claimed the killer was hired by French fashion mogul Gerald Marie, accused of multiple counts of sexual assault, to murder another, the BBC’s Lisa Brinkworth, after she went undercover to expose his agency. French prosecutors this year closed the probe because the alleged crimes took place too long ago.
Mr George’s barrister Michael Mansfield told the trial that the National Criminal Intelligence Service had a dossier which suggested the killing was in retaliation for the Belgrade TV station bombing by Nato jets which killed 17 staff.
British warplanes were attacking Yugoslavia to halt the ethnic cleansing of Albanians by Serbian forces in Kosovo. The barrister claimed that after the attack, Serb warlord Zeljko Raznatovic – alias Arkan – put out a contract on the BBC director general Sir John Birt. His security was stepped up so the target was switched to the unguarded Ms Dando.
She had earlier fronted a broadcast appealing for funds to help refugees.
The Met said: “The investigation into the murder of Jill Dando was moved to an inactive phase in 2014. The decision was taken by a case closure panel.”