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Educated at a state grammar school in London and at the University of Oxford, he trained as a fighter pilot with the Royal Air Force. He worked with an oil company in Borneo and Oman.[when?] He has worked as a social scientist on corporate social responsibility with several American and European organisations. He has written about his Buddhist beliefs.
In his television career he has been the producer, writer and presenter of many documentaries and series, particularly on science and technology. His programmes have been transmitted on networks including the BBC and Channel 4 in the United Kingdom, as well as Discovery Channel, National Geographic Channel and the Public Broadcasting Service in the US.
He is best known as a producer and presenter on the BBC's science magazine programme Tomorrow's World and on the BBC's motoring programme Top Gear. On Tomorrow's World he was a leading presenter  for 11 years, winning several awards including Top Science Presenter. He won a reputation for the enthusiasm he brought to his reports, and his skill in turning technical subjects into entertaining television.
He fronted Top Gear for a decade from 1981, during which time it became a prime time show with an audience of up to 5 million. Woollard also presented Rally Report, an offshoot of Top Gear, covering the Lombard RAC Rally every year.
Woollard resigned from Top Gear in 1991, despite protestations for him to come back, mainly because his own production company, Inca, took off, producing documentaries for BBC and C4 in the UK and channels such as the Public Broadcasting Service and Discovery Channel in the US. Among Inca's commissions were the filming of the Royal Institution Christmas Lectures.
During the same period he was involved in writing and producing or presenting a range of other programmes, mainly under the banner of the BBC science documentary strand Horizon. These included:
- The Secret War, a seven-part series that revealed the role that Britain's scientists played in the winning of the Second World War.
- Too Hot to Handle. A three-part series looking at the benefits and drawbacks of the nuclear power industry.
- The Energy Alternative. BBC television's first look at the problem of global warming, and the challenge presented by alternative energy technologies.
- Skyscraper. An award-winning five-part series on the building of a skyscraper in central New York City.
In 1986 Woollard was instrumental in setting up one of the first independent production companies, making programmes for the world's leading networks. Since that time he has written or produced well over 100 programmes ranging over the fields of science and technology, from evolution, to space exploration, and from treasure hunting to the science of bridge building.
William Woollard now[when?] works as a scriptwriter on documentaries and he has authored books including one recounting his experience as a practising Buddhist. His documentaries issued on DVD still sell widely in the UK and US.
During his pieces to camera for Top Gear, Woollard was renowned for discussing a car's engine or performance whilst standing with one foot on the front bumper of the car and with its bonnet lifted. This pose has gained a life of its own in the form of the international photographic craze known as Woollarding whereby members of the public take self-portraits with their own bonnet-up cars whilst standing with one leg on the front bumper.
- The Reluctant Buddhist, ISBN 978-1-906210-35-9
- Buddhism and the Science of Happiness: A Personal Exploration of Buddhism in Today's World, ISBN 978-1-907652-73-8
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