The son of an electrician, Norwood graduated with a history degree from Keble College, Oxford in 1988 before joining city investment bank Banker's Trust in 1991.

Norwood cofounded Oxford Sciences Innovation, a £1.2bn investment firm dedicated to creating deep science world changing companies from Oxford University, and was its CEO from 2015 to 2019.

Formerly he was founder of IP Group plc, a fund that invested in spinoffs from Oxford University's Chemistry department, in exchange for 50% of the revenues from the licensing of the department's intellectual property.

[1] In 2017, Norwood donated £1.9M to Keble College's future hub Archived 26 April 2018 at the Wayback Machine for innovation at Oxford University.

He has on a number of occasions captained, managed, or sponsored the England squad in major team events such as the Chess Olympiad.

Norwood has written several books including Winning with the Modern (the Modern Defence being a favorite opening of his) and Steve Davis plays Chess (co-authored with Steve Davis).

In the following game, Norwood's hypermodern opening leads to an old-fashioned king hunt: Norwood-Marsh, Walsall 1992[3] 1. g3 d5 2.