Theatre Heath made his professional stage debut playing the lead role of Hon. Alan Howard in a production of the
Terence Rattigan play
French Without Tears at the
Orange Tree Theatre in 2016. He also played Man in the two-hander
In the Night Time (Before the Sun Rises) at the Orange Tree Theatre in 2018. In 2019 he played the titular role of Peter Pan in a production of
Ella Hickson's
Wendy and Peter Pan at the
Royal Lyceum Theatre, directed by
Eleanor Rhode, with the show going on to receive outstanding critical reviews. In June 2024, it was announced that Heath would play Oleg Sogolyev in the world premiere of
David Edgar's new play
The New Real at the
RSC.
Film and television Heath played the role of Kazimir in British television series
Spies of Warsaw, and made his feature film debut alongside
Andrew Scott in
Mick Jackson's film
Denial. Heath then played Derby in the
Caitlin Moran-written 2019 film
How to Build a Girl. He played Sam Holland in the
period drama Harlots inspired by
The Covent Garden Ladies by British historian
Hallie Rubenhold. He played Jack Philips in the adaptation of Jessie Burton's best selling novel
The Miniaturist, and played Luke Harris in the
Cold Feet revival. He also appeared in the
Black Mirror episode "
Hated in the Nation". He portrayed the younger version of
Kindertransport humanitarian Martin Blake in the 2023 film
One Life, with
Jonathan Pryce playing the older version. The film went on to close the
Toronto International Film Festival, receiving excellent reviews. He appeared as Mark in the 2023 film
Greatest Days and plays the role of
Peggy Bettinson in the
Steven Knight historical drama
A Thousand Blows. ==Personal life==