Nothing is known of his early life or education; the title pages of two of his plays identify him as a "Gentleman," though there is no record of him at either of the two universities or the Inns of Court.
[1] His extant dramatic canon consists of only three plays: The City Nightcap, A New Trick to Cheat the Devil, and King John and Matilda.
King John and Matilda (printed 1655) bears strong resemblances to The Death of Robert Earl of Huntingdon, the second of Anthony Munday and Henry Chettle's two Robin Hood plays, and can be regarded as virtually a rewrite of the earlier work.
The subplot of this play was borrowed from Miguel de Cervantes and Giovanni Boccaccio, and Aphra Behn's Amorous Prince (1671) is an adaptation of it.
Samuel Sheppard, in a 1651 epigram, mentions a fourth lost work, The Pirate, which he thought showed how Davenport "Rival'st Shakespeare, though thy glory's lesse".