He was a son of Sir Thomas Rich, 1st Baronet, and his second wife, Elizabeth, daughter of William Cockayne, alderman and merchant of London.
In 1667, he succeeded his father as the 2nd Baronet Rich of Sonning, Berkshire, a title created in the Baronetage of England in 1661.
Rich's political interests became evident in 1680 when he accompanied the Duke of Monmouth and Lord Lovelace on a visit to Oxford.
During this period, he aligned himself with the Court Whigs and supported the disabling clause in the bill to restore corporations.
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