William Roberts was educated at Eton, St Paul's and Corpus Christi College, Oxford, where he gained his BA in 1788 and MA in 1791. He toured the Continent (including Paris) before returning to England and founding a short-lived biweekly journal, The Looker-on (1792-1793) under the pseudonym Rev. Simon Olive-Branch. Entering the law, he wrote several legal treatises. He married Elizabeth Anne Sidebotham, daughter of a Middle Temple barrister, who bore him ten children. From 1811 to 1822 he was editor of the British Review and London Critical Journal, founded by the evangelical clergyman William Weyland. Byron mocked him in Canto I of Don Juan. Roberts published his four-volume biography of Hannah More in 1834: its hagiographic tone and editorial inaccuracy drew the scorn of John Gibson Lockhart in the Quarterly, but the inclusion of extended extracts from More's letters has ensured its enduring interest to those interested in More. He retired from the law to Surrey, and later to St Albans in Hertfordshire.

His son Arthur Roberts wrote a biography in 1850.