On Clarkson's wikipedia page it says that
Clarkson's Car Years ran from 1999 to 2001. It doesnt say anything else. IMDB only lists it as one season. sorry I couldn't be any more helpfull.
http://en.wikipedia.org/wiki/Jeremy_Clarkson
http://www.imdb.com/title/tt0249284/
the second video I'm guessing is not the one you were wondering about since it is from fifth gear.