Porter grew up in South London and attended Wilson's School in Camberwell. He won a scholarship to Christ's College, Cambridge, where he studied under J. H. Plumb. His contemporaries included Simon Schama and Andrew Wheatcroft. He achieved a double starred first and became a junior Fellow in 1968, studying under Robert M. Young and lecturing on the British Enlightenment. In 1972, he moved to Churchill College as the Director of Studies in History, later becoming Dean in 1977. He received his doctorate in 1974, publishing a thesis on the history of geology as a scientific discipline. He was then appointed to the post of Assistant Lecturer in European History at Cambridge University and promoted to Lecturer in European History in 1977.
In 1979 he joined the Wellcome Institute for the History of Medicine (part of the University College, London) as a lecturer. In 1993 he became Professor of Social History at the Institute. He briefly served as its Director. In 2000, Porter published The Enlightenment: Britain and the Creation of the Modern World. He retired in September 2001, moving to St Leonards-on-Sea, where he wanted to learn to play the saxophone, cultivate his allotment and engage in some travelling. He died of a heart attack five months later, while cycling. His memorial service was on 22 April 2002 at St Pancras Parish Church.
He was married five times, firstly to Sue Limb (1970), then Jacqueline Rainfray (1983), then Dorothy Watkins (1987), then Hannah Augstein, and finally his wife at the time of his death, Natsu Hattori.
He was known for the fact that he needed very little sleep.