Sort of classic stage magician/music hall attire, I reckon - smart top-hat-and-tails, white gloves, fancy cane, no tie but an open, large-ish collared white shirt shirt and waistcoat. But with a very Doctor-y sort of twist on the look - maybe instead of a top hat it's a fedora, or something, the gloves are fingerless, his shoes really battered, and while the rest is black and white the waistcoat is red/burgandy.