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Dunn died on Tuesday (local time), Peter Charlesworth said, adding that he believed the actor died in Portugal where he has lived for many years. He was 92.
As Lance-Corporal Jones in Dad's Army - a hit television series in the 1960s and 1970s about a group of local volunteer members of the Home Guard - Dunn was famous for catchphrases such as "Don't panic!" and "They don't like it up 'em."
He also had a No 1 hit song with "Grandad" in 1971, which he performed several times on TV music show "Top of the Pops".
Dunn was born in London in 1920 and enrolled in an acting academy after leaving school.
He played several small roles in films in the 1930s before serving in the army in World War 2, ending up in prisoner-of-war and labour camps for four years.
After the war he worked in music halls before enjoying success as Jones in Dad's Army.
Underlining his ability to play characters far older than his real age, he followed Dad's Army with a five-year run in children's comedy series "Grandad" as an elderly caretaker.
According to the BBC, he is survived by his wife Priscilla Morgan and two daughters, Jessica and Polly.