Police said yesterday that they believed the killer waited for an hour outside the television presenter's home in Fulham, west London, for her to return from a shopping trip. They spoke of seven witnesses who may have seen the suspect, including a window cleaner - who thought the man was an estate agent waiting for a client - another cleaner and a mother with her child. The man made no attempt to hide or avoid being spotted, pacing up and down the road.
The Independent understands that while detectives are investigating other possibilities, they believe the killing was almost certainly committed by a professional.
Yesterday, police confirmed that Ms Dando, 37, had been shot in the side of the head at very close range with a single bullet from a semi-automatic handgun. The shot caused massive injuries and Ms Dando died a little over an hour later. The use of a hollow-pointed bullet is extremely rare.
Detectives are focusing their attention on reports of a well-groomed, smartly dressed man, carrying a mobile phone, who was seen in the road where Ms Dando lived just seconds before she was fatally wounded. The same man was seen briskly leaving the scene.
A man fitting a similar description was seen a little later climbing over railings on the bank of the river Thames a few minutes walk from Ms Dando's two-storey home. Police said the man may have been using a disguise - in particular large dark-coloured glasses which one witness noticed and said looked too big.
Then, possible a few minutes later, another man waiting at a bus stop in Fulham Palace Road saw a man running down the road. He was described as wearing a dark blue suit and sweating profusely.
Yesterday Detective Chief Inspector Hamish Campbell, the officer heading the murder inquiry, said: "At this stage we will look at every avenue. A whole range of matters will be looked at. [Ms Dando's] private life will be one of the areas that will be explored."
Det Ch Insp Campbell worked with Crimewatch, the BBC television show that Ms Dando presented, during the investigation into the murder of a 12-year-old Macedonian girl in Hammersmith, west London, in May 1997.
As a routine part of the inquiry, detectives will speak to all of Ms Dando's former boyfriends, including Simon Bassil who met the presenter on location at the Kruger National Park in South Africa where he worked as a game warden.
Detectives yesterday spoke to Mr Bassil at his home in Portsmouth, Hampshire. Now a computer analyst, Mr Bassil came to Britain from Africa in 1997. Ms Dando broke off their relationship soon after. "I have spoken to police. They have come to my house today," he said. "I found out about Jill's death from my mum. It's all speculation at the moment about her killing. I have spoken to her family and expressed my condolences."
Ms Dando was shot at around 11.45am on Monday on the doorstep of her home after returning via Hammersmith from the Chiswick home of her fiance, Alan Farthing. She was found by a neighbour who heard her scream and when he rushed downstairs he found Ms Dando slumped against the door, covered in blood and unconscious.
Det Ch Insp Campbell said yesterday that there were a number of reasons why people did not report hearing a shot. But it is understood that officers believe the killer almost certainly used a silencer. One witness reported hearing a clicking noise, a sound associated with guns fitted with such devices.
Police sources said yesterday that a semi-automatic handgun fitted with a silencer and ammunition could be bought illegally for pounds 1,000. Without a silencer the gun - most likely a Browning, Glock or a Tanfoglio - could be purchased for as little as pounds 500.
It is understood that Ms Dando's attacker used a "quarter-tipped" bullet which are designed to spread out on impact causing maximum damage. Such bullets cannot be bought legally.
Police are also investigating whether Ms Dando's killing could be the result of a grudge borne against her because of her work with the Crimewatch programme. Officers have spoken to co-presenter Nick Ross and other members of the programme's team about security in the wake of the shooting. However, their initial inquiries through police informants have revealed nothing about anyone trying to obtain a hitman "to do Jill Dando".
Officers are also investigating the possibility that Ms Dando was killed by a stalker, although they said yesterday that she had made no recent complaint.
Medical experts said that the stalker theory could be valid. They said details of her death could fit in with someone who had become obsessed by her, and who might even be suffering from De Clerembault's syndrome, a rare form of sexual obsession.
The type of gun used was banned following the Dunblane school massacre in Scotland in March 1996, but hundreds are believed still to be in circulation. Criminologist Kate Broadhurst, of the Scarman Centre for the Study of Public Order, Leicester, said: "The sawn off shotgun is the weapon of choice for the bank robber... this is the weapon of the drug dealer and the weapon of the professional criminal." The type of bullet used in the attack has only been used in a handful of incidents in Britain.
Mr Campbell said that his team was examining a range of possible motives for the murder. "It could either be a stalker or a hitman. However, there are many theories to be explored and nothing will be left untouched. Everything is being looked at."