Wehn moved to the UK in 2002 to work in the marketing department of Wycombe Wanderers FC. One evening he saw an open mic night and decided to try comedy.
Since October 2003 Wehn has been the self-styled "German Comedy Ambassador in London". After beginning his career as "warm-up act" to various comedians in London (including Stewart Lee for Comedy Vehicle), he now has his own act on the British comedy circuit.
Wehn has appeared on the panel shows 8 Out of 10 Cats, Have I Got News For You, Room 101 and QI, and also appeared on Channel 4's political discussion/comedy show 10 O'Clock Live in May 2013. He is also a recurring panellist on both the BBC Radio Five Live comedy sports show Fighting Talk and on the BBC Radio Four panel game The Unbelievable Truth.
He has also appeared on the BBC's Would I Lie to You?, on which he revealed that he spent three weeks on the Interpol missing persons list, having travelled to Morocco with a man he met on a train in Spain.
In 2014, Wehn and fellow comedian Mark Watson fronted a travelogue in Brazil, called The Road to Rio for Dave. In the show they explored the country's sporting culture, tying in with the 2014 World Cup held in the country.