Police are focusing the hunt for the killer of BBC presenter Jill Dando on a man seen outside her home before the murder.

The man detectives want to question was spotted loitering in Gowan Avenue in Fulham, west London up to an hour before the killing at 11.30am on Monday. He was then seen running from the scene in the moments immediately afterwards.

Ms Dando, 37, who presented Crimewatch UK and Holiday, was shot once in the side of the head from very close range with a 9mm semi-automatic pistol, police told a news conference in London.

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There was no sign of a struggle: Ms Dando did not even have enough time to get her keys into the door before she was shot.

Speculation that a professional hitman was involved heightened after the execution-style manner of the killing was revealed, but police are keeping an open mind.

At least seven witnesses who could have seen the man have come forward.

Detective Chief Inspector Hamish Campbell said a window cleaner had seen a man outside Ms Dando's home at about 10.30am.

He is described as being in his late 30s or early 40s, 5ft 11in tall, dark haired and wearing a suit.

An hour later and just before the shooting, nearby, another witness saw a similar man, wearing large black-framed spectacles which appeared too large for him.

Ms Dando, who had gone shopping in Hammersmith Mall after leaving her fiance's home in Chiswick at 10am, arrived home at 11.30am when she was shot.

Cmdr Brian Edwards and DCI Hamish Campbell explain the circumstances of the killing

Police said that after the killing, a man with a mobile phone had been seen running away from Ms Dando's home in Gowan Avenue towards Putney Bridge where two witnesses saw a man climbing railings at Bishop's Park, next to the River Thames.

A man sweating profusely was later seen at a bus-stop in Fulham Palace Road, but he is not thought to have got on a bus.

Police search the bank of the Thames

Detectives are expected to investigate the possibility that a criminal caught by Crimewatch UK held a grudge against her.

Experts said the pistol used - thought to be a Browning or a Tanfoglio - was the weapon of the professional criminal.

Handguns were banned following the Dunblane massacre, but hundreds are thought to be in circulation.

An obsessed fan or stalker is also a possibility. Ms Dando was allegedly stalked last year, but police said on Tuesday that she had made no recent complaints to them about a stalker.

Police said Ms Dando's previous boyfriends were being contacted and CCTV footage from the Hammersmith area was being examined.

Police are also scouring the river embankment near Bishop's Park.

Mr Campbell appealed for information from anyone who might have been involved in the illicit supply of the gun used in the shooting.

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Somebody must know if they recently provided such a weapon to somebody through the illegal network," he said.

Ms Dando's murder prompted tributes from the Queen and Prime Minister Tony Blair.

And BBC News Online received more than 9,000 e-mails from users wanting to remember the star in the hours following her death.