Educated at Thame grammar school, Knapp entered the navy, but finding the sea unsuited to his health, he resigned and served successively in the Herefordshire and Northamptonshire militia, becoming a captain in the latter.
On one of these he visited Scotland in company with Scottish botanist George Don and collected several of the rarest species of British native grasses.
In 1804 he published Gramina Britannica, or Representations of the British Grasses on 119 coloured plates, with Descriptions, in quarto, the figures being executed by himself.
Knapp viewed it as a botanical companion to Gilbert White's ‘Selborne.’ He lived till 1813 at Llanfoist, near Abergavenny, and subsequently at Alveston, near Bristol, where he died.
Rhynchoglossum, originally named by Carl Ludwig Blume, was similarly unsuccessfully renamed Knappia by Franz Bauer in 1840.