Detectives investigating the murder of Jill Dando are studying closed circuit television footage to see if anyone followed her home from her shopping trip before she was killed.

They are also constructing an electronically generated picture of the man they suspect shot the BBC presenter, but this has not yet been released.

The E-fit is being produced with the help of one of seven witnesses who saw a smartly-dressed man near the scene of the murder in Fulham, west London, on Monday.

Estate agents' files are also being traced after it emerged that Ms Dando had sold her house just days before she was murdered on its doorstep.

It is believed police want to speak to prospective buyers who visited the home to eliminate them from their inquiries.

A Metropolitan Police spokeswoman said: "We believe the sale of Jill Dando's house had just been completed.

"We're investigating all the circumstances".

Police are also searching drains near the site of the shooting in the hunt for the murder weapon.

On Tuesday police confirmed that the 37-year-old Crimewatch presenter was gunned down at close range by a man with a 9mm semi-automatic pistol. The gunman had waited up to an hour for her to return home and then fled the scene carrying a mobile phone.

He is described as a white male, wearing a dark suit, with neatly cut brown hair and aged 35 to 40.

The execution-style manner of the shooting has prompted speculation that she might have been the victim of a hitman, but police are considering several other possibilities.

Theories include that she was murdered by an obsessed stalker, was the victim of a botched robbery, or even that she was targeted by Serb extremists because of her support for the Kosovar refugees.

Police have appealed to the criminal world for leads on the illegal handgun used to murder Ms Dando as they step up their search for clues.

They have formally ruled out her fiancé, Alan Farthing, as a suspect, but they will be examining Ms Dando's private life and interviewing former partners.

The officer leading the inquiry, Detective Chief Inspector Hamish Campbell, said Ms Dando had not recently expressed any concerns about being stalked. However she did tell a police conference recently that she feared for her safety.

Officers have also found a new witness who may have come face to face with Ms Dando's killer on Gowan Avenue. The 10-year-old boy was being driven to school by his mother when he saw a "weird" man loitering just outside her home.

He has been able to draw pictures of the suspect's clothing for police.

The front of Ms Dando's house is still covered with the white tarpaulins erected by police forensic teams. Dozens of bouquets have been laid in the street outside.

Warnings for BBC stars

In the wake of the murder police have spoken to Crimewatch co-presenter Nick Ross about his security, and a general warning has been circulated to other BBC figures.

The BBC's security chief, former Detective Superintendent Eddie Halling, has advised stars how to protect themselves.

BBC News Online is still receiving e-mail tributes from users wanting to remember the star. More than 11,000 have already sent their thoughts and condolences.