He then became an announcer for domestic BBC Radio in the 1960s, presenting Serenade in the Night from January 1960 and Family Favourites from April of that same year, both on the Light Programme.
In the mid-1970s, Dunn briefly returned to his previous role as an announcer and newsreader, but he moved to his long running drive time Radio 2 programme in 1976.
After guesting on his drivetime show, writer/broadcaster Terence Pettigrew reversed their roles by inviting Dunn onto his BBC Radio 2 programme Caught in the Draft, a documentary about compulsory national service, which had originated during the Second World War and ended at the beginning of the 1960s.
In 1979, Dunn provided the BBC TV commentary at the Eurovision Song Contest, held that year in Jerusalem, and was the commentator for the United Kingdom.
He was married with two daughters, and lived in Croydon, London, where he died on 27 November 2004, aged 70, after a long battle with cancer.