Scotland Yard said that Mr Stagg was arrested at his home in Roehampton at 5.30am yesterday and was taken to Wimbledon police station where he was questioned before being formally charged. Police forensic science experts searched his flat and garden.
Miss Nickell, 23, was found dead on Wimbledon Common early on the morning of 15 July.
The killing caused widespread horror, particularly among other women who used the common. The former model, who lived near by with her boyfriend, Andre Hanscombe, had been walking on the common with their son, Alex, three, and their labrador dog.
The boy, found clinging to his mother's body and calling on her to get up, was unharmed. For 24 hours he was unable to speak and a child psychiatrist was called in to help him to come to terms with what had happened. The investigation into Miss Nickell's murder has been one of the largest and costliest conducted by Scotland Yard detectives in recent years, involving thousands of house-to-house inquiries and statements at an estimated cost of pounds 1.5m.
A lengthy undercover surveillance operation was maintained on the common in case the killer attempted to accost another woman. Police sources said the arrest involved an undercover officer. It is understood that a woman officer had formed a friendship with Mr Stagg.
The inquiry initially involved more than 54 detectives but had recently been scaled down to about a dozen. More than 30 potential suspects have been arrested and interviewed by police.
Mr Hanscombe, a professional tennis coach, now lives in France with his son; before the murder the family had been planning to leave London and make a new life there.
Earlier this summer, Mr Hanscombe and his son returned to Britain when Alex was seen by detectives and provided new information.
Earlier in the inquiry, detectives had examined possible links with other unsolved murders of women in the area, including that of Penny Bell, 43, a businesswoman stabbed in her Jaguar car outside a leisure centre in Greenford, west London, in June 1991.
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