Found this info on a website
Costume Designer Susan Matheson had great fun creating costumes for David Tennant’s character, illusionist Peter Vincent. For his stage-show look she designed a classic leather frock coat with an exaggerated collar. Then she gave him lots of rings on his fingers and some very tight, stretch leather pants with boots. For his vampire-fighting scenes, the look changed to another long leather coat with a revisionist 1980s feel, worn with a T-shirt, jeans and sneakers.