| 2005 | Foreign Member, Royal Society of Arts and Science, Göteborg, Sweden. |
| 2005 | Honorary Fellow Honoris Causa, The Worshipful Company of Gardeners, London, U.K. |
| 2004-2006 | President, Palaeontological Association, U.K. |
| 2004 | Knighted in the UK, June 2004, for services to horticulture and conservation. |
| 2004 | Honorary Doctor of Science, University of Portsmouth, U.K. |
| 2004 | Member, German Academy Leopoldina. |
| 2002-2004 | Council, The Royal Society. |
| 2002 | Honorary Fellow, Birkbeck College, University of London, U.K. |
| 2002 | Foreign Member, Royal Swedish Academy of Sciences. |
| 2001 | Hutchinson Medal, Chicago Botanical Garden. |
| 2001 | Honorary Doctor of Design, Kingston University, U.K. |
| 2000 | Honorary Fellow, Darwin College, University of Kent, U.K. |
| 2000 | Honorary Fellow, Royal Holloway College, University of London, U.K. |
| 2001 | Foreign Associate, National Academy of Sciences, U.S.A. |
| 1998-2000 | President, Paleontological Society (President Elect 1997, Past President 2000-2002). |
| 1998 | Fellow of the Royal Society, (Council 2002-2004), U.K. |
| 1998 | Henry Allan Gleason Award, New York Botanical Garden ("1998 outstanding publication in the fields of plant taxonomy, plant ecology or plant geography"). |
| 1993 | Paleontological Society, Schuchert Award. |
| 1984 | Linnean Society of London, Bicentenary Medal ("in recognition of work done by a biologist under the age of 40 years"). |
