Henry Symonds received his medical training at St Bartholomew's Hospital, London, qualifying in 1888 as Bachelor of Medicine (MB), member of the Royal College of Surgeons (MRCS) of England, and licentiate of the Royal College of Physicians (LRCP) of London. For some time he was house physician at St Bartholomew's Hospital and wrote "Medical cases" for the St Bartholomew's Hospital Report (1889). In 1890 he came to the Cape Colony, where he was licensed to practice in August that year, and settled in Kimberley as resident medical officer at Carnarvon Hospital. Three years later he qualified as Doctor of Medicine (MD) at the University of London. In 1895 he published a paper on "Tuberculosis" in the South African Medical Journal (2nd series). By 1897 he held the position of ophthalmic surgeon at Carnarvon Hospital.
Symonds was elected secretary of the Griqualand West (Kimberley) Branch of the British Medical Association in December 1895. At a meeting of this branch in February 1899 he delivered a carefully prepared paper on "Some points of interest in connection with eye diseases", a summary of which was published in the South African Medical Journal (April 1899, Vol. 6, pp. 272-273). The paper dealt chiefly with diseases of the eye frequently met with in Kimberley, particularly various forms of conjunctivitis and problems secondary to this condition. By 1898 he was a member also of the (second) South African Medical Association.
Symonds was still listed as practising in Kimberley in 1926. From 1908 to 1912 he was a member of the board of management of the McGregor Museum. He was married to Frieda Tyrell, with whom he had at least four children.