McKenna's TV work includes Yorkshire Television's The Brides in the Bath, Waking the Dead, The Bill, Judge John Deed, Spooks, Lead Balloon, Waterloo Road, and Life Begins. Alan is also a recurring character in Little Miss Jocelyn. He played Detective Inspector Phil Crabtree in the 2014 crime drama Happy Valley. He voiced various characters in the video game Titanfall.
His film work includes Blessed with Heather Graham, David Hemmings and Andy Serkis. Second in Command alongside Jean-Claude Van Damme, An American Werewolf in Paris with Julie Delpy and Dangerous Parking.