Leppard was born in London and grew up in Bath. He studied harpsichord and viola at Trinity College, Cambridge, where he also was active as a choral conductor and served as music director of the Cambridge Philharmonic Society.
In 1952 he made his London debut and then conducted his own Leppard Ensemble. He became closely associated with the Goldbrough Orchestra, which became the English Chamber Orchestra in 1960. He also gave recitals as harpsichordist, and was a fellow of Trinity College and a lecturer on music from 1958 to 1968.
His interest in early music prompted him to prepare several realisations of scores from the period. While musicologists considered his editions controversial, his performances were important for introducing early operatic masterpieces to the general public. His production, Monteverdi's L'incoronazione di Poppea, was presented at the Glyndebourne Festival under his direction in 1962. In the following years he subsequently prepared more operas by Monteverdi, as well as operas by Cavalli.
In November 1969, he made his USA debut conducting the Westminster Choir and New York Philharmonic, at which occasion he also appeared as soloist in the Haydn's D major Harpsichord Concerto. In 1973 he became principal conductor of the BBC Northern Symphony Orchestra in Manchester, he position he retained until 1980.
Leppard has also conducted Britten's Billy Budd at the Metropolitan and San Francisco Operas, Alceste and Alcina at the New York City Opera. He has also conducted at the Royal Opera House, Covent Garden and in Paris, Hamburg, Santa Fe, Stockholm, and Geneva.
At Glyndebourne, he conducted the world premiere of Nicholas Maw's Rising of the Moon. Over the past decade, Leppard has been music director of the Indianapolis Symphony Orchestra.
Raymond Leppard has been honoured by The Queen with the CBE. In 1973 the Republic of Italy conferred upon him the title of Commendatore della Republica Italiana for services to Italian music.