The star of new parenting show Bringing Up Baby got some Satisfaction from the wrinkly Rolling Stone with his then wife Jerry Hall just YARDS away.
Claire, now 41, had been employed to take care of the superstar couple's son Gabriel, then seven months old. But while Jerry played with the tot in the next-door bedroom, Jagger swaggered into the kitchen of his hotel suite.
And as quick as Jumpin' Jack Flash he plonked Claire on the worktop and told her 'Get Yer Ya-Yas Out'.
Claire describes herself as a "total bitch" on the Channel 4 show and is a firm believer in old-fashioned values. But that soon went out the window with legendary rock stud.
She recalled: "I was making coffee when Mick came in. The kitchen was so small we kept bumping into each other.
"I enjoyed the closeness. Suddenly, Mick was stroking my hair, then we were in each other's arms.
"He hitched me up on to the breakfast bar and pulled down my jogger bottoms. We kissed passionately and the next thing I remember he was making love to me."
She continued: "It was all over very quickly and Mick carried on as though nothing had happened. He kissed me on the nose and said, 'OK, babe.' A few minutes later he was laughing with Jerry and cuddling little Gabriel.
"I stood with a cup of coffee in my hand thinking, 'My God, what was that all about?'
"He was obviously used to doing that sort of thing. But I wasn't offended. I was with one of the sexiest stars on the planet."
Hours earlier Claire--who's also looked after the kids of Sting and Dire Straits star Mark Knopfler and once gave Princess Diana baby advice -had arrived at the couple's hotel in Brussels. She had been hired to look after Gabriel during a Stones' European tour.
She said: "I walked in the bedroom. The baby was on the bed with Jerry who was in a bath robe.
"Then the shower curtains parted and to my amazement Mick Jagger stepped out, stark naked. Jerry didn't bat an eyelid. But I didn't know where to put my eyes and I dropped my bags in surprise.
"He stuck out his hand and said, 'Hi, I'm Mick.' I didn't know which bit to shake!
"He was very slim but he looked lean and fit. He obviously looked after his body and he's pretty well endowed.
"He didn't seem embarrassed. There I was, a village girl from Kirkby Overblow in Yorkshire standing before rock's greatest superstar. He was dripping with water, but he had this aura."
It wasn't the last time Claire had a close encounter with Mick, now 64. She said: "We're both cricket fans and sat down to watch it on TV. We became all touchy-feely again and I have to admit I was really up for it.
"But there were too many people around, including Jerry, that we never got down to it."
Claire, then became pals with Texan model Jerry-all the while carrying her guilty secret about her romp with Mick.
She said: "We often went shopping together, picking up the kids from school-all the things that girlfriends do together.
"She was very generous. But I never knew whether she suspected what had happened. I felt she knew about all the other episodes in his life."
Jerry, 51, filed for divorce in 1999-a year after Claire's fling-after discovering his adultery with Brazilian model Luciana Morad.
Claire says she doesn't regret her kitchen fumble. "Mick's got a certain magic about him. I couldn't resist."
And while she recommends a hands-off approach to stop kids becoming clingy, one dad was definitely very much hands-on.