Wilkinson trained at the Royal Academy of Dramatic Art before making his West End debut portraying Horatio in Hamlet (1980) for which he received a nomination for the Laurence Olivier Award for Best Actor in a Supporting Role.

[2][3][4][5][6] At the age of 11, he moved with his family to Kitimat, British Columbia, in Canada,[7] where they lived for five years before returning to the United Kingdom and running a pub in Cornwall.

[13] In 1993 he had a small role as an Appeal Prosecutor, Grant Richardson in Jim Sheridan's biographical crime drama In the Name of the Father starring Daniel Day-Lewis and Emma Thompson.

[16] Wilkinson had a small but important role as the dying father, Mr. Dashwood, in the Ang Lee-directed Sense and Sensibility (1995), and played a villain in the adventure drama The Ghost and the Darkness (1996).

[18] In 1998 he acted in the British romantic costume drama Shakespeare in Love starring Gwyneth Paltrow, Joseph Fiennes, Geoffrey Rush, and Judi Dench.

[19] Wilkinson won wider critical acclaim for his portrayal of grieving father Matt Fowler in Todd Field's film, In the Bedroom (2001),[20] with co-stars Sissy Spacek and Marisa Tomei.

[22] The following year he played Dr. Howard Mierzwiak in the Michel Gondry directed science-fiction romantic comedy Eternal Sunshine of the Spotless Mind (2004) starring Jim Carrey and Kate Winslet.

Also in 2010 he starred in the John Landis directed horror comedy Burke and Hare and portrayed a covert CIA agent in Roman Polanski's The Ghost Writer.

The following year he acted in the British comedy The Best Exotic Marigold Hotel starring opposite Judi Dench, Bill Nighy, Dev Patel, and Maggie Smith.

David Rooney of The Hollywood Reporter praised his performance writing, "Observed with sensitivity and played with a deep well of sorrow by Wilkinson, this story breathes real tenderness into the movie's reflections on growing older and making peace with past mistakes".

The following year Wilkinson portrayed Lyndon B. Johnson, the 36th President of the United States, in Ava DuVernay's historical drama film Selma (2014), and had a role in Wes Anderson's comedy The Grand Budapest Hotel (2014).

In 2016, he portrayed journalist Ewen MacAskill in Snowden starring Joseph Gordon-Levitt and barrister Richard Rampton in Denial acting alongside Rachel Weisz and Timothy Spall.