This portrait bust of Dr Antonio Cocchi (1695-1758) was commissioned from the sculptor by Francis, 10th Earl of Huntingdon (1729-1789), and was recorded at his seat, Castle Donington, Leicestershire, in 1768, along with three other busts, including a portrait of the Earl himself, also by Wilton. Although Cocchi sat to the sculptor in Florence in 1755, and the bust is signed and dated that year, it has recently been argued that it was completed after Wilton's return to England in 1756.

The pairing of this bust with that of Lord Huntingdon at the Earl's seat probably commemorated the friendship between the Florentine doctor and the Englishman on his Grand Tour. The medallion on the front of the socle gives the sitter's name and age (60), the date, and the statement 'I go on learning as I grow old'. The serpent biting its tail symbolises perseverance, as well as being an attribute of medicine.

Joseph Wilton (1722-1803) was the son of a London plasterer and manufacturer of papier-mâché ornaments, but received his training as a sculptor on the Continent, first under Laurent Delvaux at Nivelles, and then under Jean-Baptiste Pigalle in Paris. He went to Florence in 1751, and remained there until his return to England in 1755. In 1768 he became a founder member of the Royal Academy, but on inheriting a large legacy from his father he neglected sculpture and was declared bankrupt in 1793. In 1796 he was appointed Keeper of the Royal Academy, a post he retained until his death.

Dr Cocchi was an eminent Florentine physician, the friend of many Englishmen in Florence, and a notable scholar; he edited the first printed version of Benvenuto Cellini's autobiography in 1728, and was keeper of the Grand-Ducal collections in Florence from 1738 until his death. In 1722 he had travelled to England as the guest of the 9th Earl of Huntingdon, the father of the 10th Earl. He was a close friend of the British envoy in Florence, Horace Mann. Mann's friend, Horace Walpole, commented to a correspondent in 1740, 'I am very well acquainted with Doctor Cocchi; he is a good sort of man, rather than a great man; he is a plain honest creature with quiet knowledge, but I dare say all the English have told you, he has a very particular understanding.

This marble bust was made after a plaster model, and almost certainly Wilton's original studies were made from the life. Wilton was well-acquainted with Cocchi, as both men gave guide lectures around the collections in the Uffizi and the Pitti Palace in Florence. If, as seems likely, the bust was actually carved in marble on Wilton's return to England, he probably left Italy with a plaster version to use as the model. A bronze version of the bust surmounts Dr Cocchi's tomb in the church of Santa Croce, Florence.