Ledwith moved to London to study acting at the Royal Academy of Dramatic Art (RADA).
Ledwith's first role after leaving RADA was in the Royal Court production of The Future Is Betamax at the Ambassadors Theatre in London's West End.
His most recent stage role was as Sir Arthur Conan Doyle in Harvey Weinstein's production of Finding Neverland directed by Rob Ashford at the Curve theatre, Leicester.
In 2001–2002, Ledwith was a regular in Holby City (BBC) playing the part of Fr Michael, who committed suicide after having an illicit affair with a nurse.
He has worked with actors and directors on a variety of projects including Spider-Man: Far From Home, Daredevil, Rogue One: A Star Wars Story, The Night Of, The Crown, The Collection, Salem, Deadpool, Snatch, The Americans, Pride and Prejudice and Zombies, Jason Bourne, Top Boy, Boardwalk Empire, Green Room, Guardians of the Galaxy, Humans, Quantico, '71, Prince of Persia, The Woman in Black, The Impossible, One Day, The Suspicions of Mr Whicher and Downton Abbey.