Burrows was educated at Prescot Grammar School and Brasenose College, Oxford, where he received his BA (First Class, Martin Wronker Prize for the best result in Law Finals 1978), which was later promoted to MA, and subsequently took the BCL (First Class).

He was a lecturer at the University of Manchester from 1980 to 1986, a fellow and lecturer at Lady Margaret Hall, Oxford from 1986 to 1994, a visiting professor at Bond University and research fellow at ANU in 1994, and a Law Commissioner for England and Wales from 1994 to 1999.

This led to the Contracts (Rights of Third Parties) Act 1999, which significantly reformed the law of contract in England & Wales and Northern Ireland by providing for a statutory exception to the common law doctrines of privity and (indirectly) consideration.

[4] He was then appointed as the Norton Rose Professor of Commercial Law at St Hugh's College, Oxford.

[8] In private practice, Burrows was a door tenant of Fountain Court Chambers, London.