Shawe-Taylor is the son of Brian Newton Shawe-Taylor and Jocelyn Cecilia Shawe-Taylor. He was educated at Shrewsbury School, University College, Oxford, and the Courtauld Institute of Art in London.
Shawe-Taylor was a lecturer in the History of Art Department of the University of Nottingham from 1979 to 1996, and director of Dulwich Picture Gallery from 1996 to 2005, when he was succeeded by Ian Dejardin. He has published several books: Genial Company: the theme of genius in eighteenth-century British portraiture, 1987; The Georgians: eighteenth-century portraiture and society, 1990; Dramatic Art: theatrical paintings from the Garrick Club, 1997; Rembrandt to Gainsborough: masterpieces from Dulwich Picture Gallery, 1999; Shakespeare in Art, 2003; Bruegel to Rubens: masters of Flemish painting, 2007; and The Conversation Piece: scenes of fashionable life, 2009.
He was made redundant in December 2020, following the news that the Royal Collections Trust "expects to lose £64m in income this year because Buckingham Palace and other sites have been shut to visitors." 
In 1987, Shawe-Taylor married Rosemary North. They have three children: Marianne, Edward and William.
- "Queen's art experts leave as Covid hits royal finances". 23 December 2020 – via www.bbc.co.uk.
- "Appointment of new Surveyor of The Queen's Pictures", The Royal Collection, 17 December 2004, accessed 22 May 2008
- "Shawe-Taylor, Desmond Philip", Who's Who 2010, A & C Black, 2010; online edition, Oxford University Press, December 2009; online edition, November 2009, accessed 1 June 2010 (requires subscription)
| Director of Dulwich Picture Gallery
| Surveyor of the Queen's Pictures