His most notable roles have been in One Summer (1983), Backbeat (1994), Land and Freedom and Nothing Personal (1995), Michael Collins (1996), Liam (2000), as Professor Quirrell in Harry Potter and the Philosopher's Stone (2001), as Ludwig van Beethoven in Eroica (2003), My Mad Fat Diary (2013–2015), as Father Beocca in The Last Kingdom (2015–2020), and as Carl in The Responder (2022).

In 1995, Hart portrayed a POUM militia volunteer in Ken Loach's Spanish Civil War film Land and Freedom.

[3][1] In 2003, Hart and fellow actor Linus Roache fasted for three months and lost 2 stones each, to achieve a malnourished look for the filming of Blind Flight, where he played Middle-Eastern hostage Brian Keenan.

The same year, Hart worked alongside John Simm at the Duke of York's Theatre production of Andrew Bovell's play Speaking in Tongues.

[1] In 2022, Hart was back in Liverpool playing drug dealer Carl Sweeney, in the BBC One British police drama series The Responder alongside Martin Freeman.