Aldridge's first professional acting role was in a play The Master and Margarita at Lyric Theatre, Hammersmith in 2004. In 2008, Aldridge made his television debut in Channel 4's four-part miniseries The Devil's Whore, playing Harry Fanshawe, husband of the title character. That same year, he was featured on Screen International's "Stars of Tomorrow" list. In addition to First Light, Lewis, Toast and Vera, Aldridge also appeared as Daniel Parish in the BBC One period drama Lark Rise to Candleford. In 2011, the American network The CW cast Aldridge as the lead in the pilot Heavenly. Later on he spent time in Belgrade shooting the partially improvised romance short film In the Night for director Ivana Bobic and cinematographer Rain Li, alongside supermodel Danijela Dimitrovska.
Aldridge is a co-founder of "In the Corner Productions". He directed the comedy pilot Pet Shop Girls in late 2011, which he co-wrote and co-produced with actor-writers Luke Norris, Ed Hancock and Kirsty Woodward.
In 2013, Aldridge starred in Almeida Theatre's production of American Psycho as Paul Owen, opposite Matt Smith, Susannah Fielding, Jonathan Bailey, and Lucie Jones. The musical thriller featured a book by Roberto Aguirre-Sacasa based on Bret Easton Ellis's cult novel, with music and lyrics by Duncan Sheik. In September 2014, he joined BBC's original drama series Our Girl as Captain James. He left the role after the third series in 2018. In December 2014, Aldridge joined The CW's series Reign as King Antoine of Navarre.
More recently, Aldridge has starred in Fleabag (2016–2019), Pennyworth (2019–2023), Spoiler Alert (2022) and Knock at the Cabin (2023).
