They believe the gun had never been fired before the day in April when the 37-year-old television star was shot at point-blank range on the doorstep of her London home.
Their new theory explains why ballistic experts have not been able to match the 9mm bullet to a particular type of weapon and it throws doubt on the speculation that she was killed by an underworld hitman.
When a bullet is shot through a gun barrel it is left with tell-tale grooves on the head and the casing unique to the type of weapon. There was no such rifling on the killer's bullet, leading detectives to draw the conclusion it was fired from a crude, handmade weapon.
"Anyone with a lathe and some basic engineering skills could either use a replica weapon as a blueprint to make a gun, or convert a replica weapon into the real thing. There are probably around one million blokes in this country who have the capabilities and the equipment at home to make such a weapon. It's frighteningly easy," revealed one officer close to the inquiry.
In the early days after the 26 April shooting there was speculation that Miss Dando had been shot by a Serb in retaliation for the Nato bombings or killed by a Russian Mafia crime boss who had been publicly spurned by her. Both theories have now been dismissed as "complete rubbish" by the enquiry team.
The prime suspect is not the "sweating man" featured in the E-fit photograph issued by police but a man in a waxed jacket who was seen walking quickly down Gowan Avenue after the murder. He was described as being tall and smartly dressed with a mop of thick black hair. Criminologist Mike Presdee said: "If the killer is a real loner he is going to be very, very difficult to trace. He is obviously a skilled worker, has a lathe at home, knows a little bit about weapons and is skilled at metalwork. Not many professional people would have these skills.
"He could possibly be a former gun club member who is bright enough and has the ability to carry off this crime undetected. If he was going to brag about it he would have done it by now ... that magical period has gone for the police where killers leave taunting messages and deliberate clues.
"The trouble is, although Jill Dando probably had a small circle of real friends, millions of people thought that they knew her and it would be impossible for the police to interview everyone.
"They are trying to find a pattern but there doesn't appear to be one. There is no set model for a stalker, they comes from all social classes and backgrounds, male and female. If the man was obsessed with Miss Dando he is highly unlikely to strike again."
One of the country's leading gun makers, who asked not to be identified, said: "Even the rebels in Afghanistan can make superb weapons from simple hand tools.
"A replica handgun costing pounds 30 would provide an easy pattern to work from. It is very easy to make a gun, even if it only fires once. A pistol called the Liberator, made during the war, consisted of a block of wood, a tube and elastic band and it only fired once.
"It is quite possible that the gun that killed Miss Dando was such a crude weapon."
Anyone with information should call the incident room on 0181-246 0732 or Crimestoppers on 0800 555 111.