The late broadcaster - who has been accused by many women of sexual abuse throughout the 1960s and 1970s - is said to have angered Sophie Rhys-Jones when she worked as a PR at London's Capital Radio in 1990.
Rhys-Jones - who later married Prince Edward in 1999 - was reportedly chosen to meet Savile when he joined the radio station.
DJ David Hamilton alleged that the pair stood for photos when her skirt blew up, prompting Savile to "shower" her with kisses.
"She greeted Jimmy with champagne, even though he was teetotal," Hamilton told the Daily Star.
"The pictures were to be done outside Capital Radio on one of the windiest corners in London. The next thing you know, the wind has blown up her skirt, but it made Jimmy all the more tactile.
"The more this happened the more amorous Jimmy became, showering her with kisses."
He added: "Sophie stormed off and said, 'I refuse to have anything to do with that revolting man'. Jimmy was very, very disappointed.
"I remember him saying, 'I started with a pretty girl and now I'm left with you, a hairy gorilla'."
Sir Jimmy Savile's £4,000 gravestone was removed from a Scarborough cemetery yesterday "out of respect for public opinion".
The BBC will hold an independent inquiry into the abuse allegations made against Savile.