Crane was born in Hastings, East Sussex, but grew up in Norfolk. He attended Wymondham College from 1967 until 1972, then Cambridgeshire College of Arts & Technology (CCAT), a forerunner to Anglia Ruskin University, where he studied geography.

In his youth, he went camping and hiking with his father, and explored Norfolk by bicycle, which gave him his enthusiasm for exploration.

In 1986, he located the pole of inaccessibility for the Eurasia landmass travelling with his cousin Richard; their journey being the subject of the book Journey to the Centre of the Earth. In 1992-3, he embarked on an 18-month solo journey, walking 10000 kilometres from Finisterre to Istanbul. He recounted the trip in his book Clear Waters Rising which won the Thomas Cook Travel Book Award in 1997, and made a television self-documentary of the journey: High Trails to Istanbul (1994).

His 2000 book, Two Degrees West, described his walk across Great Britain in which he followed the eponymous meridian as closely as possible. Most recently he published a biography of Gerard Mercator, the great Flemish cartographer.

Together with Richard Crane, he was awarded the 1992 Mungo Park Medal by the Royal Scottish Geographical Society for his journeys in Tibet, China, Afghanistan and Africa.

In November 2007 he debated the future of the English countryside with Richard Girling, Sue Clifford, Richard Mabey and Bill Bryson as part of CPRE's annual Volunteers Conference.

He married Annabel Huxley in 1991, they live in Chalk Farm, in north-west London, and have three children.