The film and TV star died peacefully on Saturday surrounded by his family, his agent said.
A message from Sutton’s family said: “Today we’re devastated by the loss of our beautiful Dudley, who leaves a gaping hole in all our lives.
“We’re grateful for the love expressed by friends and fans everywhere and for the extraordinary care he received at the Royal Trinity Hospice in Clapham, south London, where he went out fighting for our NHS.”
Sutton starred opposite Ian McShane in the BBC comedy-drama series throughout its 70-episode run from 1986 to 1994. His played a tout who was friends with the antique dealer played by McShane.
Chris Jury, who played Eric Catchpole in the show, led tributes on social media.
He wrote: “My dear, dear pal Dudley Sutton died today. I loved him dearly. Condolences to Fanny, Peter, Barnaby, Wally and Jacqueline and all the rest of his family… Love you Duds.”
Inbetweeners actress Emily Atack appeared in the 2011 comedy film Outside Bet alongside Sutton. She shared a photo on Instagram of herself and Sutton on the film’s set with the late actor Bob Hoskins.
She wrote: “So sad to hear Dudley Sutton has passed. Such a hilarious, warm, talented man who I’m so honoured to have worked with. Sending love to his family who he spoke of always.”
Spandau Ballet musician and actor Gary Kemp added: “Farewell Dudley Sutton. One of our greats and a charming man.”
Sutton’s other TV appearances included a special Christmas episode of BBC sitcom Porridge and an instalment of ITV crime drama The Sweeney.
In his later career he had a recurring role as conman Wilfred Atkins in BBC soap EastEnders, as well as smaller parts in Holby City and Channel 4 teenage drama Skins.
Sutton joined theatre director Joan Littlewood’s Theatre Workshop group and appeared in numerous plays that portrayed working class life during the 1950s and 1960s.
Sutton’s breakout screen role came in the 1964 film The Leather Boys, in which he played a gay biker.
He later appeared in films such as The Devils (1971), The Pink Panther Strikes Again (1976) and The Football Factory (2004).