“I can’t remember last week — let alone 25 years ago. But I know this much, I have never, ever taken advantage, or anything else like that, of a woman."
He added that he expects to be "completely exonerated" by the police investigation.
The father-of-five also recounted an encounter with a dancer who got so drunk at a pantomime after show party he gallantly gave up his bed and slept on the floor.
He claims: “I never laid a finger on her even though she was completely comatose and wouldn’t have had a clue what was going on.
“That’s what kind of bloke I am — I’m a gentleman.”
Davidson, who was arrested at Heathrow Airport after flying back to the UK to take part in Celebrity Big Brother, said he was "totally gobsmacked" by what had happened.
His solicitor said previously the allegations date back approximately 25 years.
Scotland Yard is leading a national investigation into allegations against disgraced television presenter Savile and a number of other high-profile figures.
Detectives have separated the inquiry into three strands: claims against Savile, those involving Savile and others, and those involving others.
So far, officers have questioned people including former pop star Gary Glitter, comedian Freddie Starr and PR guru Max Clifford.
Last month, police said a total of 31 allegations of rape had been made against former Top Of The Pops presenter Savile.
Some 589 people have come forward with information relating to the scandal, with a total of 450 complaints against the BBC presenter and DJ, mainly alleging sexual abuse.
Detectives have recorded 199 crimes in 17 force areas in which Savile is a suspect.
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Jimmy Savile Abuse Timeline
(01 of24)
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Jimmy Savile in 1961 around the time he was working for Radio Luxembourg. He is at London Airport with Pan American stewardess Birgit Johansson with two gold discs; one is for American singer Elvis Presley for having sold one million copies of "It's Now or Never" in the UK, and the other is for Presley's manager, Colonel Tom Parker (credit:PA)
(02 of24)
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Cilla Black and Jimmy Savile before a Variety Club Luncheon at the Savoy Hotel. Taken in 1964, the year Savile became the first presenter of Top of the Pops (credit:PA)
(03 of24)
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Two women have come forward with allegations from the 1960s, one who was 14 and another who was a teenager when she claims Savile sexually abused her in Scarborough (credit:PA)
(04 of24)
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Savile in 1969 with Physically Handicapped and Able-Bodied (PHAB) member Erika Mentz from Germany and other PHAB members at a dance at Devonshire House (credit:PA)
(05 of24)
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1969 also saw Savile begin volunteering at the Stoke Mandeville Hospital for specialist spinal injuries. He would later be given a room there (credit:PA)
(06 of24)
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Jimmy Savile presenting a cheque to children on behalf of the NSPCC in 1969 (credit:PA)
(07 of24)
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The 1970s saw Savile start volunteering at Leeds General Infirmary and... (credit:PA)
(08 of24)
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... Broadmoor secure high-security psychiatric hospital. Allegations by former patients have been made against Savile although ex-workers have disputed the idea that he could have been left alone with anyone whilst working there (credit:PA)
(09 of24)
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The 70s also saw the start of Jim'll Fix It. Allegations from this period include Caroline Moore, a 13-year-old patient at Stoke Mandeville hospital in 1971, who says Savile "rammed his tongue" down her throat and another allegation accuses Savile of molesting a brain-damaged teenage patient at Leeds General Infirmary in 1972 (credit:PA)
(10 of24)
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The 1980s saw the continuation of Top of the Pops and Jim'll Fix It as Savile became a much loved household name. Two allegations relating to this time include one from a then-15-year-old girl (not pictured) who made a complaint of abuse by Savile in Lancashire. Pictured is 12-year-old Rebecca Heap (credit:PA)
(11 of24)
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Savile at the Stoke Mandeville hospital with injured children from Beirut in 1987 (credit:PA)
(12 of24)
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Savile was knighted in 1990 and continued his charity work throughout the decade (credit:PA)
(13 of24)
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Savile was questioned in 2007 by police about allegations of sexual abuse but the Crown Prosecution service says there is not enough evidence to warrant a prosecution (credit:PA)
(14 of24)
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A 2008 police report into abuse at the Haut de Garenne children's home in Jersey names Savile, although this is never made public (credit:PA)
(15 of24)
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Savile re-united with his Jim'll Fix It chair in 2009. The previous year Sussex police received a complaint of sexual assault but went on to say the victim was "unwilling to co-operate in any investigation" (credit:PA)
(16 of24)
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Jimmy Savile is found dead at the age of 84 in October 2011. He is buried in Scarborough (credit:PA)
(17 of24)
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In December 2011 the BBC drop an investigation by Newsnight into the allegations of sexual abuse by Jimmy Savile. Three tribute programmes are aired instead (credit:PA)
(18 of24)
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ITV airs a documentary, 'Exposure, the Other Side of Jimmy Savile', in which a number of women claim they were abused by Savile as youngsters, including Karin Ward (pictured) (credit:ITV)
(19 of24)
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Within days of the documentary, many more allegations surface. By the 9 October Peter Spindler of the Metropolitan Police tells the BBC: "It is quite clear from what women are telling us that Savile was a predatory sex offender" (credit:PA)
(20 of24)
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11 October 2012 and George Entwistle, Director General of the BBC, asks journalists why the Newsnight programme was dropped as police from Tayside, Greater Manchester, Lancashire and North Yorkshire police say they are investigating allegations going back to 1959 (credit:PA)
(21 of24)
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12 October and police reveal they have 340 potential lines of inquiry (credit:PA)
(22 of24)
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15 October sees a man come forward alleging that Savile abused him when he was a nine-year-old boyscout (credit:PA)
(23 of24)
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Savile's family removed his headstone from his grave and broke it up in the wake of the furore (credit:PA)
Jimmy Savile sexually abuses transgender man(24 of24)
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A transgender man comes forward alleging that Jimmy Savile 'stuck his hand up his nightdress' while he was a 17-year-old teenage girl at Broadmoor in the 1970's. More here http://www.huffingtonpost.co.uk/2012/10/15/jimmy-savile-timeline-abuse-allegations_n_1966426.html?1350304573#slide=1641388 (credit:PA)