Frederick Parham was born on 9 January 1901, son of Frederick James Parham, and Jessie Esther Brooks Parham (née Robertson). He was educated at the Royal Naval Colleges at Osborne [Isle of Wight] and Dartmouth [Devon]. He married 1st, in 1926, Kathleen Dobrée (she died in 1973), daughter of Eugene Edward Carey, and had one son; and married 2nd, in 1978, Mrs Joan Saunders (née Charig).

Parham joined HMS Malaya as Midshipman in 1917, later going on to specialise in gunnery, in 1925. He was made Commander in 1934, commanding HMS Shikari (1937) and then HMS Gurkha (1938-40). Promoted to Captain in 1939, his next ship was HMS Belfast (1942-44), followed by HMS Vanguard (1947-49). Made Rear-Admiral and naval aide to the King in 1949, Parham became Deputy Chief of Naval Personnel (1949-51), then (as a Vice-Admiral from 1952), Flag Officer (Flotillas) and 2nd in command, Mediterranean (1951-52). Parham served as a Lord Commissioner of the Admiralty, Fourth Sea Lord and Chief of Supplies and Transport (1954-55), before becoming Commander-in-Chief, The Nore (1955-58); he retired in 1959. His honours included: GBE 1959 (CBE 1949); KCB 1955 (CB 1951); DSO 1944. He died on 20 March 1991.