The son of Sir Hugh Griffiths was educated at Charterhouse School and St John's College, Cambridge. During the Second World War he served in the Welsh Guards, receiving a Military Cross in 1944. Griffiths was called to the Bar, Inner Temple in 1949, and became a Queen's Counsel in 1964. From 1962 to 1964, he was Recorder of Margate, and from 1964 to 1970 of Cambridge. In 1971, Griffiths was knighted and was made Judge of the High Court of Justice, Queen's Bench Division, a post he held until 1980. Between 1980 and 1985, he was Lord Justice of Appeal, and between 1985 and 1993 Lord of Appeal in Ordinary, created additionally a life peer with the title Baron Griffiths, of Govilon, in the County of Gwent on his appointment.
Griffiths has married twice, first Evelyn Krefting in 1949, and after her death in 1998, he married second Heather Renwick Brigstocke, the former High Mistress of St Paul's, on 22 January 2000. She was killed in a car accident in 2004. He has four children by his first wife: three daughters and one son.