After graduating from the Royal Acadamy of Dramatic Art in 1985, Watkins joined the National Theatre Company and went on to be nominated for an Olivier award for Best Supporting Actor for his turn in A Servant For Two Masters (2000). His theatre credits in the years since include playing serial killer Ralph in the play Frozen (Theatre Royal Haymarket), as well as The Twits (Royal Court Theatre), Strange Interlude (National Theatre), Farewell to the Theatre (Hampstead Theatre), and A Laughing Matter (National Theatre). In 2025, Jason stars in The Seagull at the Barbican Theatre in London. 

Watkins is perhaps best known for his contributions to award-winning, critically acclaimed British and international TV drama series such as his lead role in the two-part drama The Lost Honour of Christopher Jefferies, for which he won the BAFTA TV Award for Best Actor. He has also played William Herrick in Being Human, Gavin Strong in Trollied, Simon Harwood in W1A, British Prime Minister Harold Wilson in The Crown and Detective Sergeant Dodds in McDonald & Dodds. He has also made notable appearances in iconic British programmes including Doctor Who, Call the Midwife and Line of Duty. In 2025, Watkins will take on the role of Huw Miller in upcoming Channel 5 four part thriller, Catch You Later. 

In film, Watkins is known for his comedic appearances as Charles Parker-Knowles in Bridget Jones: The Edge of Reason, Mr Nellist in teen comedy Wild Child, and the eccentric school teacher Mr Gordon Shakespeare in the family Christmas comedy series, Nativity. In 2023, Watkins played Mr. Treading in the British black comedy, Wicked Little Letters. 

Watkins, and wife Clara Francis are Patrons of Child Bereavement UK following the loss of their beloved daughter, Maude to sepsis in 2011. Watkins has become a key voice in raising awareness of sepsis and fronted an ITV documentary in 2023 Jason and Clara: In Memory of Maude which followed their journey as parents grieving the loss of a child.