Although Hudd and Kay had made a brief appearance as 'discoveries' on the BBC's In Town Tonight in 1958, Hudd made his solo debut on radio in 1959 on Workers' Playtime. He remains best known for the BBC Radio 2 satirical series The News Huddlines, which ran from 1975 to 2001. His other radio credits include playing Max Quordlepleen, the host at The Restaurant at the End of the Universe, in the original radio series of The Hitchhiker's Guide to the Galaxy, Crowned Hudds, The Newly Discovered Casebook of Sherlock Holmes and Like They've Never Been Gone.
Television
Hudd broke into television in the mid-1960s in sketch series such as The Illustrated Weekly Hudd and The Roy Hudd Show. His acting roles include the Dennis Potter series Lipstick on Your Collar, for which he received critical praise, and Karaoke. In the mid 1990s he appeared in two series of Common As Muck, a drama about a group of refuse collectors, alongside Edward Woodward. In 2000 Hudd appeared as neighbour Mr. Smedley in one episode of One Foot in the Grave. From 2002 to 2003, he appeared as the undertaker Archie Shuttleworth in the ITV soap opera Coronation Street and subsequently returned for guest appearances in 2006 and 2010; the character died offscreen in December 2018. He also starred in the ITV drama 'The Quest', alongside Sir David Jason and Hywel Bennett, from 2002–2004. In 2007 he appeared in episodes of New Tricks, Casualty and The Last Detective. In 2010 he appeared in BBC dramas Missing and Ashes to Ashes. In 2012 he appeared in an episode of the BBC drama Call the Midwife. In 2014 he appeared in episodes of Midsomer Murders, and Holby City. In December 2015, Hudd played Bud Flanagan in the BBC drama We're Doomed! The Dad's Army Story, about the creation of the titular long-running sitcom. In 2016 he appeared in an episode of Benidorm. In 2017 he appeared in the ITV series Broadchurch.
Hudd wrote several books on music hall, re-recorded music hall records, and appeared in the music hall revival show The Good Old Days. He was seen by broadcasters as an authority on the subject and was the longstanding President of the British Music Hall Society. His CD, Mirth, Magic and Melodrama consists of a collection of classic monologues from the music hall days, including The Pig and The Lion and Albert, first recorded by Stanley Holloway. For Celebrity Mastermind, broadcast in January 2014, Hudd answered questions on the specialist subject of music hall comedian Dan Leno. He was an authority on the comedian Max Miller and was known for his impersonation of Miller. He appeared as his hero in the Big Finish ProductionsDoctor Who audio play Pier Pressure in 2006. He was President of the Max Miller Appreciation Society.
Charity work
Hudd had a long association with the Bristol Hospital Broadcasting Service, where he was considered an honorary member. In 1994 he officially opened their current studios in the Bristol Royal Infirmary. He was also a past King Rat of the show business charity the Grand Order of Water Rats. In addition to this, he was the first Honorary President of Sandwell Hospital Radio in West Bromwich for a period of ten years, visiting the studios, members and patients whenever he was appearing in the West Midlands.
Death
On 16 March 2020 Hudd's agent announced his death on 15 March, aged 83, following a "short illness".