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In August 1963 she appeared in the West End in London, New Zealand and Broadway, in the Cambridge University revue Cambridge Circus directed by Humphrey Barclay, alongside Graham Chapman, John Cleese, Bill Oddie, Tim Brooke-Taylor, David Hatch and Chris Stuart-Clark.
Moving to radio comedy she was a regular performer in the BBC's I'm Sorry, I'll Read That Again (with John Cleese, Tim Brooke-Taylor, Bill Oddie, Graeme Garden and David Hatch), and a member of the panel in the very first edition of I'm Sorry I Haven't A Clue. Kendall was also a regular team member of the popular radio comedy series The Burkiss Way and played Lady Cynthia Fitzmelton in the opening episode of The Hitchhiker's Guide to the Galaxy. In 1978 she appeared in the comedy drama The Unvarnished Truth at London's Phoenix Theatre with Royce Ryton, Tim Brooke-Taylor and Graeme Garden. In 1993 and 1994 she played Aunt Maud opposite Kate Copstick in the BBC children's series Marlene Marlowe Investigates.
Kendall has also appeared in 'straight' drama. She appeared as Adelaide Palliser in The Pallisers (1974), as the matron, Miss Biggs, in the film version of Scum (1979), as Annie in the film adaptation of Howards End (1992), directed by James Ivory, and as a publican's wife in another Merchant Ivory film The Remains of the Day in 1993. Among her television roles, she played Mrs. Bardell in The Pickwick Papers (1985), Anne Stanhope in The Six Wives of Henry VIII and had a semi-regular part in Grange Hill in the 1980s as the mother of regular character Roland Browning. In addition, she played the abrasive Miss Elizabeth Wait in the BBC's adaptation of the Vivien Alcock book The Cuckoo Sister (1986).
Further information about Kendall can be found in the books:
- From Fringe to Flying Circus — 'Celebrating a Unique Generation of Comedy 1960-1980' — Roger Wilmut, Eyre Methuen Ltd, 1980.
- The Clue Bible — 'The Fully Authorised History of I'm Sorry I Haven't a Clue from Footlights to Mornington Crescent' — Jem Roberts, Preface, 2009.
- The Times Newspaper, May 9, 1962