The 50-year-old was yesterday alleged by the Sunday Mirror to have cheated on Frances, his manager and wife of 18 years.
However, the Top Gear presenter has now said that he enjoyed a "lovely lunch" with his wife and three children for Mother's Day, adding: "I'm surprised to find that I'm the new Tiger Woods."
According to The Sun, a friend commented: "He's stunned by these claims. He's been working hard on Top Gear for a while and is enjoying a holiday with his family.
"As far as we're concerned life is going on as usual."
Father-of-three Clarkson writes a regular column for The Sun, in which he recently revealed that the BBC had banned him from serving up a barbeque to Louis Spence and Al Murray.