But the television programme-makers who arranged the test claimed that he had changed his mind about fielding further questions under the influence of a "truth drug" and resisted the opportunity of giving his testimony under hypnosis after learning that both were more reliable tests of honesty.
Mr Stagg, 33, agreed to meet the television journalist Roger Cook for the first public assessment of his defence to the charge of Ms Nickell's murder in 1992 on Wimbledon Common, London.
Mr Stagg's defence was never heard in court after the judge dismissed the case against him, and the same case cannot be brought for a second time. But in The Cook Report, to be broadcast tonight, Mr Stagg claims he would welcome a civil action against him. "If the Nickell family was convinced I was innocent, that would make me more at ease with my life.
"I would like to meet the family and look them straight in the eye and tell them plainly I'm not guilty of this murder," he says.
Mr Cook, however, appeared sceptical about some of Mr Stagg's responses, including his refusal to take the "truth drug" - a mixture of benzodiazepines or sedatives - on medical grounds. Mr Stagg said he feared the long-term effects of having such chemicals in his body.
Mr Cook concluded: "Stagg gave us his full co-operation for an investigation into his side of the story and his legal team gave us complete access to his defence case. [But] There are still inconsistencies and questions unanswered."
Mr Stagg faced 60 questions in the polygraph lie-detector test. The test, which is not permitted as evidence in British courts, was administered by Jeremy Barrett, who categorically concluded that Mr Stagg did not kill Ms Nickell.
However, in at least one instance, the programme-makers claim Mr Stagg gave an answer which contradicted his response in a previous polygraph test which he also passed.
Mr Cook then questioned similarities between Mr Stagg's sexual fantasies - as described in letters to an undercover policewoman known as Lizzie James - and the attack on Ms Nickell.
In his letters, Mr Stagg described having fantasies about sex with strangers, nakedness on Wimbledon Common, the use of knives and dripping blood. But he claimed another man with the same fantasies must have been responsible for the attack. "The difference between the man who did this and me is that he has these fantasies and he acts out his fantasies. It's somebody much more dangerous than me, because he believes in these fantasies and these are just stories I have made up off the top of my head," Mr Stagg said.
He also disputed evidence of his whereabouts on the day of her murder and claimed not to be a violent man. Witnesses Susan Gale and Jane Harriman both described seeing Colin Stagg between 9.25am and 10.23am on the day Ms Nickell died. But Mr Stagg insisted he was home after his own walk on the common long before that - and before the time that the killing is believed to have taken place.
And he accused police of being "dirty bastards". "You know they set people up," he said.
Derek Crussell, the hypnotherapist who tried to hypnotise Mr Stagg, said he believed Mr Stagg was capable of being hypnotised but had not allowed himself to be. Steve Clark, head of factual programmes for Carlton Television, said Mr Stagg was paid no fee but received travelling expenses not exceeding pounds 2,000 for the month's work in Birmingham and London.
The programme is due to be broadcast on ITV at 8.30pm tonight.