Hogwood was born in Nottingham. He studied music and classical literature at Pembroke College, Cambridge. He went on to study performance and conducting under Raymond Leppard and Thurston Dart; later Rafael Puyana and Gustav Leonhardt. The British Council enabled him to study in Prague for a year.
In 1967 he founded the Early Music Consort with David Munrow, and in 1973 founded the Academy of Ancient Music, which specializes in performances of baroque and early classical music with period instruments. Hogwood continues to perform and record with that ensemble but he also guest conducts with many other orchestras.
Since 1981, he has been conducting regularly in the United States. Hogwood is conductor laureate of Boston's Handel & Haydn Society.
From 1983 to 1985 Hogwood was the artistic director of the Mostly Mozart Festival in the Barbican Centre in London. From 1987 to 1992 he was the musical director of the Chamber Orchestra of Saint Paul (Minnesota), which appointed him as its principal guest conductor.
Hogwood also conducts much opera. He made is operatic debut in 1983, conducting Don Giovanni in Saint Louis He has worked with Berlin State Opera, Royal Opera Stockholm, Royal Opera House Covent Garden, Chorégies d’Orange and Houston Grand Opera. With the Opera Australia, he performed Idomeneo in 1994 and La Clemenza di Tito in 1997 Iphigenie auf Tauris.
Although Hogwood is best known for the baroque and early classical repertoire, he also performs contemporary music, with a particular affinity for the neo-baroque and neoclassical schools including many works by Stravinsky, Martinu and Hindemith.
Since 1992 Hogwood has been international professor of Early Music Performance at the Royal Academy of Music, and a visiting professor at London's King's College.
Hogwood has written a number of books, including a BBC Music Guide on the trio sonata (1979) and a biography of George Frideric Handel (1985).