Today With Des and Mel was an ITV daytime chat show that went from 2002-2006. The hosts were:

• Des O’Connor (67 episodes)
• Melanie Sykes

Jimmy Carr appeared on the episode that aired December 19^th 2005 according to IMDB and his Management Company Website (click on Credits, which also indicates a 2004 appearance).

Despite a LOT of different ways of searching – I cannot find any images or video.

Previously Jimmy had appeared on Des O’Connor Comedy Tonight in 2003.

In 2005 Jimmy had finished his Public Display of Affection tour and had embarked on Off The Telly. This TV appearance would not have been quite as exciting as the one in January 2006, when he got to travel to the US to appear on Conan (again).