Webb appeared on the BBC Radio 4 programme "Desert Island Discs" in May 1982. She selected the "Piano Concerto No.1 in B Flat Minor" by Tchaikovsky; "Una voce poco va" from "The Barber of Seville"; "The Swan" from "The Carnival of the Animals"; "Oh Happy Day" by the Edwin Hawkins Singers; "Layla" by Derek and the Dominos; "Bridge Over Troubled Water" by Simon & Garfunkel; and "Space Oddity" by David Bowie. Her favourite selection was a recording of "The Dreaded Batter Pudding Hurler of Bexhill-on-Sea" from "The Goon Show". She also chose to take an illustrated dictionary and piano to her imaginary island.