His scabrous wit appeared to have deserted him when confronted at his mansion in Chipping Norton, Oxon, about the alleged law-breaking, however.
He at first denied being in the car but when shown the photo said: "That isn't a mobile phone."
He then slammed the front door and shouted: "Look, I write a column for another newspaper. I'm not allowed to talk to you."
The father-of-three has had several brushes with the law in recent months.
In September he was acquitted in a speeding case after hiring celebrity lawyer Nick Freeman, known as "Mr Loophole".
A V6 Alfa Romeo Brera which had been loaned to the presenter by the manufacturer was caught doing 82mph in a 50mph zone in Ruislip, west London. But the case was dropped at court because it couldn't be proved who was driving.
A month later, Clarkson and fellow Top Gear host James May were told they were to be investigated by a local authority for flouting laws about smoking in the work place after lighting up on TV.
Millions of viewers saw the pair puff on pipes in the studio near Godalming, Surrey, while discussing the branded goods car makers use to sell their products.
And in December, he found himself at the centre of another investigation by Thames Valley Police after grappling with a hooded teenager who shouted at him as he left an entertainment complex in Milton Keynes, Buckinghamshire.
The force later decided to take no action as there was "no evidence a crime took place".
