In 1987 Evets was injured in a pub brawl and spent time on a life support machine. He was stabbed through the liver, lung and diaphragm, was glassed in the face and had his throat cut.

In between acting roles, he worked under the name Adolph Chip-pan, performing political comedy poetry in Manchester. He also worked as a musician, and was introduced to Mark E. Smith of the Fall in the mid-1990s, leading to Evets performing his poetry at some Fall gigs. When Smith found that Evets could play bass guitar, he was drafted into the band in Turkey after previous Bassist Jim Watts had been sacked. Evets played in The Fall between 2000 and 2002, before leaving to front his own band, Dr Freak's Padded Cell, which he described as "electronic dance music with sort of very political overtones", even getting Smith to provide guest vocals on one track; Evets made a video for the track and posted it on YouTube, much to the dislike of Smith, ending their friendship.

His first major film role came in 2008, playing a terminally-ill wheelchair-bound alcoholic opposite Robert Carlyle, in Summer. He followed this with the lead role in Ken Loach's 2009 film, Looking for Eric; his performance saw him tipped for the Best Actor award at the 2009 Cannes Film Festival.

In 2010 to 2014 he appeared as the homeless drug addict Colin in the acclaimed TV series Rev. He played Morty in Vertigo Films' 2012 low-budget horror film The Facility (originally titled Guinea Pigs) directed by Ian Clark. He starred in a music video for Salford-based band Emperor Zero's 2011 song "Man with Red Eyes".

In 2015 Evets' appeared as Jim Smith in the BBC TV series Death in Paradise episode 4.5 and he also appeared as Bertrand in the BBC TV series The Musketeers episode 2.5 "The Return". In February 2016, he appeared in the BBC One drama series Moving On.