Davenport was born in Lambeth on 18 January 1777,[1] and started work as a writer in London at an early age.
In the late 1790s he knew John Britton and Peter Lionel Courtier through a debating society, the "School of Eloquence".
[2][3] Davenport wrote large portions of the history, biography, geography, and criticism in Rivington's Annual Register for several years (1792 to 1797, according to John Britton).
[2] He edited, with lives, a number of the British poets for the Chiswick Press edition in 100 volumes (1822); the biographies were supplied from the existing ones Samuel Johnson, with Davenport, Samuel Weller Singer, and some others, writing the rest.
[2] For the last 11 years of his life Davenport lived at Brunswick Cottage, Park Street, Camberwell, a freehold house of which he was the owner.