Hancock regularly works in radio. She has been a semi-regular contestant on the BBC Radio 4 panel game "Just a Minute" since 1967. She starred as Alice Foster in the BBC Radio 2 comedy series "Thank You, Mrs Fothergill", in 1978–79, alongside Pat Coombs. In 1995 Hancock provided the voice of Granny Weatherwax in BBC Radio 4's adaptation of Terry Pratchett's Discworld novel "Wyrd Sisters". In 2011, Hancock appeared in the BBC Radio 4 series "North by Northamptonshire", alongside Geoffrey Palmer.