His surname was originally Hunt; Bonavia was a family name that was inserted as a forename as it had been his mother's maiden name. Henry Hunt's mother, originally Marietta, but later Mary, was Maltese and the daughter of a doctor of Italian extraction. Hunt became known in later times as Bonavia-Hunt and by the time his son, the Revd Noel Aubrey Bonavia-Hunt, was writing vast quantities on the subject of the organ and organ building between 1910 and 1960, the family name was firmly established as "Bonavia-Hunt". Another member of the family, D. A. Bonavia-Hunt was an author and her work is still in print.
In 1872 Hunt founded an organisation that was at first known as the Church Choral Society and it had as its object the promotion of higher standards of church music, within the background of the Oxford Movement. The standard of church music had been poor in England for much of the 19th century. Hunt had been studying law until the foundation of the Church Music Society, but abandoned this to take on this work. He engaged the help of a number of organists and choirmasters, including E. J. Hopkins, Goss and Richard Willing. By the following year, 1873, the society had become known as the College of Church Music and a system of examinations was in place. In 1876 the college was incorporated as Trinity College of Music. In 1878 a further development was the foundation of the Masonic Lodge Trinity College Lodge No. 1765 of the United Grand Lodge of England. This was the beginning TCM's long association with Freemasonry. Although the college still has a strong connection with Freemasonry, there are no Trinity men in the Trinity College Lodge, though Trinity College Lodge remains strong. William Ewart Gladstone was involved in the college in its early years. Hunt was known in his time for his considerable powers of focus and for his organisational ability. He was the editor of Cassell's Magazine from 1874 to 1896. His writings were published and are still available through archives and he was a regular correspondent to the Musical Times over the years and indeed, these may be easily viewed through the JSTOR system. Hunt studied at Oxford and at also took a degree from Trinity College Dublin. He was a composer and a lecturer for London University. The Trinity College of Music has moved to buildings of unparalleled beauty and historical importance. There is an integral partnership with the distinguished dance school, Laban. Further, the College now owns the Blackheath Concert Halls nearby. The Rev'd Henry Hunt would be astonished to see how his Trinity College of Music, which began as a simple Church Music Society, has grown and flourished, thanks to a long succession of able and energetic principals.