The veteran TV presenter said Morgan's comments were not true, claiming that he only ever took work if he would "enjoy it".
"Piers Morgan - how rude!" Chegwin told DS. "Turning around and saying, 'Keith Chegwin turns up at the opening of a fridge'. I put him to challenge on that one.
"I've turned down more work than I'm offered, for the main reason that I don't think it's going to be fun. Everything I do - it sounds a bit big-headed - I choose to do."
He added: "Even on the corporate side of things, if someone calls me up with a fantastic corporate gig, if I wasn't going to enjoy it, I wouldn't just turn up and take people's money - I don't do that."