I've never thought of Joe Dempsie being that wizard (just because I can't see any similar facial characteristics), and I originally found that information on a Harry Potter fandom: it's Ian Brown.
He's also pictured as this wizard on his IMDB page and credits :
For those unaware, Ian Brown is not an actor. He was lead vocalist with a band from the late 80s/early 90s, The Stone Roses, who were a major influence on a lot of the Brit Pop movement of the 90s. This music scene in the UK was known as "Madchester", a portmanteau of Manchester, the city many of these bands originated, & a local term for 'I really like this', "I'm mad for it".
By a series of coincidences, Brown knew a girl who knew the director… & it happened that Daniel Radcliffe was a fan, so he managed to 'blag'* a cameo.
Possibly because they shared a music scene, a fashion style, a geographical & musical origin …& also knew each other well, Ian Brown could often be mistaken for Liam Gallagher from Oasis -
*Blagging, in the UK , especially inside the music or film industry, is not to gain something by deception, but to gain entry to somewhere or something you wouldn't ordinarily be invited to by 'knowing someone who knows someone who can get you through the door'. The US equivalent may be 'schmoozing'.
Culturally, you could consider The Stone Roses to be as important to the history of music in the UK as Nirvana were in the US.