Dudley is the son of William Stuart Dudley and his wife Dorothy Irene (née Stacey). He attended Highbury Grammar School.^[1]

He was educated at Saint Martin's School of Art and the Slade School of Art. He is a member of the Society of British Theatre Designers. He is married to the theatre director Lucy Bailey.^[2]

National Life Stories conducted an oral history interview (C1173/27) with Dudley in 2007–2008 for its An Oral History of Theatre Design collection held by the British Library.^[3]

He designed his first production in October 1970, Hamlet for Nottingham Playhouse. Since then, he has designed the following productions:

• The Duchess of Malfi (Royal Court) – 1971
• Man Is Man, Bertolt Brecht (Royal Court) – 1971
• Anarchist (Royal Court Upstairs) – 1971
• Tyger (co-designed for the National Theatre) – July 1971
• Cato Street (Young Vic) – 1971
• The Good Natur'd Man (National) – 1971
• Live Like Pigs (Royal Court Upstairs) – 1972
• I Claudius (Queen's Theatre) – 1972
• The Baker, the Baker's Wife and the Baker's Boy (Newcastle) – 1972
• Rooted (Hampstead Theatre) – March 1973
• Magnificence; Sweet Talk and The Merry-Go-Round (Royal Court) – 1973
• Ashes (Open Space) – January 1974
• The Corn is Green (Watford Palace) – 1974
• Twelfth Night, director Peter Gill (RSC Stratford) – August 1974
• Harding's Luck (Greenwich Theatre) – December 1974
• Fish in the Sea (Half Moon Theatre) – February 1975
• As You Like It (Nottingham Playhouse) – 1975
• The Fool (Royal Court) – 1975
• The Norman Conquests (Berlin) – 1976
• Small Change, Peter Gill (Royal Court) – July 1976
• As You Like It (opening of Riverside Studios) – May 1976
• Ivanov, director David Jones (RSC Aldwych Theatre) – September 1976
• The Cherry Orchard, director Peter Gill, (Riverside Studios) – January 1978
• That Good Between Us (RSC Donmar Warehouse) – July 1977
• Lavender Blue (National, Cottesloe) – November 1977
• Touched (Nottingham Playhouse at the Old Vic) – September 1977
• The World Turned Upside Down (National, Cottesloe) – 2 November 1978
• Has 'Washington' Legs? (National, Cottesloe) – 29 November 1978
• Billy Budd (The Metropolitan Opera House, New York) – 1978
• Dispatches (National, Cottesloe) – 6 June 1979
• Undiscovered Country (National, Olivier) – 20 June 1979
• Lark Rise and Candleford (National, Cottesloe) – 1979
• Don Quixote (National, Olivier) – 1982
• Schweyk in the Second World War, Bertolt Brecht (National, Olivier) – 1982
• Small Change (National, Cottesloe) – 1983
• Cinderella, Pantomime (National, Lyttelton) – December 1983
• The Mysteries: Doomsday/The Nativity/The Passion, designed and lit (National, Cottesloe; Lyceum Theatre) – 1985
• The Party (RSC The Pit) – 1985
• Richard III (RSC Barbican Theatre) – 1985
• Today (RSC The Pit) – 1985
• Mutiny, David Essex musical (Piccadilly Theatre) – 1985
• The Critic/The Real Inspector Hound (National, Olivier) – 1985
• Edmond, David Mamet (Royal Court) – 1985
• The Merry Wives of Windsor (RSC Barbican Theatre) – 1986 and 1987
• Futurists (National, Cottesloe) – 1986
• Prairie du Chien/The Shawl (Royal Court Upstairs) – 1986
• Kafka's Dick (Royal Court) – 1986
• Country Dancing (RSC The Pit) – 1987
• Richard II (RSC Barbican Theatre) – 1987
• Entertaining Strangers (National, Cottesloe) – 1987
• Girlfriends, Howard Goodall musical (Playhouse Theatre) – 1987
• Waiting for Godot (National, Lyttelton) – 1987
• Cat on a Hot Tin Roof (National, Lyttelton) – 1988
• The Shaughran (National, Olivier) – 1988 and 1989
• The Changeling (National, Lyttelton) – 1988
• The Father, August Strindberg (National, Cottesloe) – 1988
• The Voysey Inheritance (National, Cottesloe) – 1989
• Cat on a Hot Tin Roof (dir Howard Davies) New York – 1990
• Lenny (dir Peter Hall) Queens Theatre - July 1999 ^[4]
• Amadeus (dir Peter Hall) Old Vic – October 1998; New York – 1999
• Blue/Orange by Joe Penhall (dir Roger Michell), National Cottesloe – April 2000; Duchess Theatre – April 2001
• All My Sons by Arthur Miller (dir Howard Davies) National Lyttelton – July 2000; National Lyttelton – August 2001
• Entertaining Mr Sloane (dir Terry Johnson ) Arts Theatre – January 2001
• The York Realist (written and dir Peter Gill) Royal Court – January 2002; Strand Theatre – March 2002^[5]
• The Coast of Utopia: Voyage/Shipwreck/Salvage, trilogy by Tom Stoppard (dir Trevor Nunn) National – August 2002^[6]
• The Breath of Life by David Hare (dir Howard Davies) Theatre Royal Haymarket – October 2002^[7]
• Honour by Joanna Murray-Smith (dir Roger Michell) National Cottesloe – 2003
• Hitchcock Blonde (written and dir Terry Johnson) Royal Court and Lyric Theatre – 2003^[8]
• The Permanent Way by David Hare (dir Max Stafford Clark) National Cottesloe – January 2004 [1]
• Cyrano de Bergerac (dir Howard Davies) National Olivier – April 2004^[9]
• Old Times by Harold Pinter (dir Roger Michell) Donmar Warehouse – July 2004^[10]
• The Woman in White musical by Andrew Lloyd Webber (dir Trevor Nunn) Palace Theatre – September 2004;^[11] New York – 2005^[12]
• Titus Andronicus (dir Lucy Bailey) Shakespeare's Globe – 2006^[13]
• The Beggar's Opera (dir Lucy Bailey) Open Air Theatre, Regent's Park – 2011
• Fortune's Fool (dir Lucy Bailey) The Old Vic – 2013.^[14]

Awards include:

• Critics' Circle Theatre Awards 2002, Best Designer for The Coast of Utopia Trilogy
• Olivier Awards 2004, Olivier Award for Best Set Design for Hitchcock Blonde

Dudley was appointed Officer of the Order of the British Empire (OBE) in the 2021 New Year Honours for services to stage design.^[15]

• Who's Who in the Theatre (17th Edition), Gale (1981). ISBN 0-8103-0234-9.
• The National: The Theatre and its Work 1963–97 by Simon Callow, Nick Hern Books (1997). ISBN 1-85459-323-4.
• Theatre Record and its annual Indexes.
• Stage Design by Tony Davis, Rotavision SA (2001). ISBN 2-88046-506-0.

• William Dudley at the Internet Broadway Database  
• British Theatre Guide interview, June 2003: "William Dudley, possibly Britain's top Theatre Designer"