Woodeson attended a prep school in Sussex before Marlborough College, where he started performing as an actor. In 1968 he read English at the University of Sussex, and with Michael Attenborough, Jim Carter, Andy de la Tour, and others, he became involved in student drama productions. He took part in the 1970 National Student Drama Festival. Next was a season in rep at the Lyceum Theatre. He won a scholarship to the Royal Academy of Dramatic Art.

Woodeson is a veteran television actor. His first network television work was playing a US marine in A Rumor of War (1980) starring Brad Davis. He played killer, Michael Hennessy, in the very first episode of Cracker (1993) Mad Woman In The Attic, starring Robbie Coltrane. He played SS-Gruppenführer Otto Hoffman in the acclaimed BBC/HBO production Conspiracy (2001), starring Kenneth Branagh, Stanley Tucci and Colin Firth. He portrayed Harman Grisewood, Assistant Director General of the BBC, in the 2008 TV programme Filth: The Mary Whitehouse Story. He has guest starred on series such as Miami Vice, Midsomer Murders, A Touch of Frost, Foyle's War, and Poirot. In the two 2005/06 HBO/BBC TV series of Rome, he played Posca, the personal slave, confidant, and aide-de-camp of Julius Caesar. In 2010 he appeared as Alexander Grozin, President of the fictional Eastern European state of Turgisia, in DR television production of Borgen. In 2013, he played Dr. william Corcoran, a proponent of Lamarckism, in an episode of Ripper Street. In 2014, he appeared as Volkov in the American miniseries The Assets, and as Algernon Wyse in a BBC TV adaptation of E. F. Benson's Mapp and Lucia. In 2016, Woodeson played the role of Reverend Matthew Denning in the BBC TV series The Living and the Dead. He has also appeared in episodes of Holby City.

Woodeson plays the Lawyer, Thoyt in the BBC One 2017 television drama series Taboo.