As a sculptor of statues, monuments and chimney pieces, Cheere studied under Robert Harsthorne, the elder and worked along side Henry Scheemakers and Louis François Roubiliac, as well as closely with John Cheere  (born 1709, died 1787), his younger brother.
Henry Cheere had a sculptors' yard located in St. Margaret's Lane, Westminster and was adept in the media of bronze, lead, marble and stone. Many of his works were rococo in flavour.
Cheere was knighted in 1760 and created a baronet in 1766. He retired from business in 1770 and travelled to Italy. A sale of the contents of his yard was held 26 March that year.
Cheere died on 15 January 1781 and was buried beside his wife, Helen Randall (died 25 October 1769), in the family vault in Clapham. He was survived by their two sons: the Reverend William Cheere, second baronet (died 1808), and Charles (died 1799).
Craske, Matthew and Malcolm Baker, ‘Cheere, Sir Henry, first baronet (1702-1781)', Oxford Dictionary of National Biography(Oxford: Oxford University Press, Sept 2004; online edn, Jan 2008) [accessed 23 May 2008].
Gunnis, Rupert, Dictionary of British Sculptors 1660-1851, New and Revised Edition (London: Murray's Sales and Service Co., 1968), pp. 97-99.
Webb, M. I. , ‘Henry Cheere, Sculptor and Businessman and John Cheere - I', The Burlington Magazine, Vol. 100, No. 664 (Jul., 1958), pp. 232-240.
'Henry Cheere, Sculptor and Businessman and John Cheere - II', The Burlington Magazine, Vol. 100, No. 665 (Aug., 1958), pp. 274-279.
‘Henry Cheere, Henry Scheemakers, and the Apprenticeship Lists', The Burlington Magazine, Vol. 99, No. 649 (Apr., 1957), pp. 115-120.