McGavin studied Zoology at the University of Edinburgh from 1971 to 1975, followed by a PhD in entomology at Imperial College, London. He went on to teach and research at the University of Oxford. He is Honorary Research Associate at Oxford University Museum of Natural History and the Department of Zoology of Oxford University, where he lists his interests as "Terrestrial arthropods especially in tropical forests, caves and savannah. Public understanding of science. Exploration." He is also a visiting professor of entomology at the University of Derby.
McGavin is a Fellow of the Linnean Society and of the Royal Geographical Society, and has several insect species named in his honour. He was previously Assistant Curator of Entomology at Oxford University's Museum of Natural History.
McGavin has lectured at the Cheltenham Science Festival, given the Royal Geographical Society children's Christmas lecture and contributes to their Schools Programme. He won Earthwatch's "Irreplaceable – The World's Most Invaluable Species" debate, broadcast on BBC Radio 4, in 2008 and he is a lecturer on board Cunard ships.
He is a patron of the charity Wildscreen, of the Bees, Wasp and Ants Recording Scheme and of the Alderney Records Centre; and is a Global Ambassador for Earthwatch and given the prize-giving speech at Stewart's Melville College
He enjoys eating insects, which he describes as "flying prawns".
McGavin was a presenter for the BBC and Discovery Channel US series Expedition Borneo (2007), and was co-presenter of the BBC series Expedition, for which he has conducted three expeditions: Lost Land of the Jaguar (2008), Lost Land of the Volcano (2009), and Lost Land of the Tiger, in Bhutan (2010). He is also a regular contributor to The One Show (BBC1) and has appeared on the Richard & Judy show to cook and eat insects.
He was Series Consultant and a contributor on Infested (Granada/ITV, 2002) and was the Chief Scientific Consultant for the David Attenborough series Life in the Undergrowth.
His other TV appearances include What's up Doc? (STV), Tomorrow's World (BBC), Package Holiday Undercover (ITV), Facing the Music (BBC), Take One Museum (Channel 4) and various national and local news programmes.
His programme Afterlife: The Science of Decay was screened by the BBC on 6 December, 2011.
From July 2011, another BBC programme, The Dark, about the nocturnal activities of animals, was produced. This started transmission on BBC2 on 29 July 2012 and on BBC HD a day later. In October 2012, he appeared, with co-presenter Dr Alice Roberts in the BBC series Prehistoric Autopsy. In 2014, he presented Monkey Planet and a two-part series on BBC Four: Dissected: The Incredible Human Hand and Dissected: The Incredible Human Foot.