Born the son of Henry Jackson (linen manufacturer and bleacher) and Jane Jackson (née Tee) of Barnsley was educated in Chester and then at Stubbington House School near Fareham in Hampshire, Henry Bradwardine Jackson joined the Royal Navy as a cadet in the training ship HMS "Britannia" in 1868. He was made a midshipman in the armoured frigate HMS "Hector" in the Reserve Fleet in April 1870 before transferring to the corvette HMS "Cadmus" in December 1871. Promoted to sub-lieutenant on 18 October 1874, he was posted to the corvette HMS "Rover" on the North America and West Indies Station in August 1876. Promoted to again to lieutenant on 27 October 1877, he joined the corvette HMS "Active" on the Cape of Good Hope Station in March 1878 and saw action ashore during the Anglo-Zulu War in 1879. He attended the torpedo school HMS "Vernon" in 1881 and, after qualifying as a torpedo officer, joined the directing staff there.