Colin the dachshund

He isn't the same dachshund as the one Stephen Fry is holding named Clover while he is driving Hugh Laurie crazy ("a cheese and tommy-toe toastie!") in the Vet sketch of A Bit of Fry and Laurie, is he?

I realize there is more than one dachshund in England, :) but thought maybe Colin/Clover was Hugh Laurie's pet?