Successful visit to the PRO uncovered James Graham full naval record from the age of 14 in 1857.
CS 19887B was his record from 26 April 1872 to 31 Dec 1872. He joined on the Duke of Wellington as 2nd captain D Dec, moving to the Hercules where he ended up as Captain of the mast.
CS35078 was an earlier record from 30 Sept 1857 when he joined on the Blenheim as a 14 year old boy. He signed his name with quite a flourish. His character was good and very good throughout. After the Blenheim he served on the Hannibal 1858/59, Conqueror 1859, Iris 1859 -1861, Orpheus 1861 - 1863, Miranda 1863, Curacoa 1863 -1867, Minotaur 1867 - 1870 and finally Trafalgar 1870 - 1872 before rejoining on the Duke of Wellington . One of my grandmother's cousin's stories is right as he did serve in New Zealand as the Iris, Orpheus, Miranda, Curacoa were all at the Australian station during the years he was on them according to the Navy lists.
Where to look next for his father though I don't know? All I have so far is his name - also James Graham, and his occupation in 1869- a silversmith.