Even in the current golden age of innovative television, the popular British crime drama “Peaky Blinders” has set a daring standard for its use of music, with original songs by Nick Cave, Laura Marling, Johnny Cash, the White Stripes and many more. Composer, music director, producer and artist Antony Genn, whose sprawling career has included stints with Pulp, Joe Strummer, Elastica and his own group The Hours, is responsible for the show’s music since season four, and brings a refreshingly punk attitude to an often sedate musical form that adds even more grit to the already gritty Cillian Murphy-starring show.

Genn’s musical career began in his teens when schoolfriend Jarvis Cocker asked him, “Do you fancy playing bass in our band?” “I don’t know how to play bass,” Genn replied. “Don’t worry about that, none of us can really play.” As is shown by this...