Knapton was born in Christchurch, Hampshire, the son of William Knapton Esquire of Brockenhurst, Hampshire. He studied art under Jonathan Richardson, then at the St Martin's Lane Academy. He spent some years in Italy where he became known as a sound judge of the works of the Old Masters. An account of his visit to Herculaneum was published in the "Philosophical Transactions" of 1740 (no. 458).[2]
Knapton assisted his brothers John and Paul, who had succeeded to and extended their father's book publishing business in London in the production of several publications including works by Thomas Birch and The History of England by Nicolas Tindal and Paul de Rapin.[2]
Knapton died in Kensington in December 1778 and was buried there on the 28th of that same month.[2]
Knapton's brother, Charles Knapton, born in Christchurch, Hampshire (1700–1760), was also an artist and, together with Arthur Pond (1705?–1758), published a book Imitations of the Italian Masters (1735), which contained many engravings by himself, mainly of works by Guercino.[2]