Frederick was born in Cambridge and was the third son of solicitor Stephen Adcock (1803-1867) and his wife Johanna (née Poland) (1805-1883).
He went to the Perse School, Cambridge and then to Jesus College Cambridge. He studied Law and obtained his L.L.B in 1866 and his L.L.M in 1869. He did not go to Jesus College until 1862 and was already working as a solicitor before entering University life.
He married widow Fanny Hardwicke at St George’s Church, Hannover Square in London on 31 January 1859. They had at least three children: Laura Belle (1861-1922), Emma Robinson (1862-1875) and Richard Robinson (1865-1905). He practised at 7 Regent Terrace (1861) and was widowed in 1867 when he was 32 years old.
He married for a second time to Mary Moseley at St Mark’s Church, Tollington Park, London on 3 May 1870, and was widowed for a second time in 1875. He died at his home at 30 Regent Street aged 47 years old.