Ralph Ambrose Kekwick was born on 11 November 1908 at Leytonstone, Essex. Records of the Kekwick family go back to 1750, when they were living near Warrington in the parish of Daresbury. They were then Quakers and were involved in the local dye industry. In about 1800 they started to move south, and Ralph's grandfather, John Kekwick (1815–82), lived first in Abingdon and then, after the death of his first wife, moved to Bromley-by-Bow, where he worked as a corn factor. A second marriage outside the sect made him unacceptable to the Society of Friends and thus broke the family association with the Quakers. John Kekwick had two daughters and six sons by his second wife; of these, Ralph's father, Oliver A. Kekwick (1865–1939), was the youngest but one. He eventually became a managing clerk in a firm of ships' chandlers in Albert Docks, London. Ralph's maternal great-grandfather, James Price (1820–1900) had an administrative post at the Guildhall, London, and was responsible for the organization of the Lord Mayor's procession and banquets at the Guildhall. His eldest son, James Price (1840–1911), Ralph's grandfather, followed his father into employment at the Guildhall. James Price had three daughters and a son; Ralph's mother, Mary E. Price (1868–1958) was his eldest child. At the age of 13 she became a pupil-teacher at Bromley St Leonard's Church school, Bromley-by-Bow, where she had been a scholar. She was compelled to give up teaching when she married in 1898, in accordance with the regulations then in force, but she was called back to teach in Leyton during World War I at a boys' elementary school and, although Essex reinstated their ‘no married women’ rule after the war, London County Council had less strict regulations and she continued to teach until she reached retirement age. Ralph was the youngest of her three children; she had an elder boy, Leslie Oliver (1899–1975) and a girl, Phyllis Mary (1902–78); with her strong character and interest in education she was a considerable formative influence in Ralph's early life and had taught him to read before he started school.
Ralph attended infants' and elementary schools in Leytonstone and then in 1919 gained a scholarship to Leyton County High School for boys. He remembered two outstanding masters, W.F. Woolner-Bird, who taught mathematics, and W.E. (later Sir Emrys) Williams, who aroused his interest in English literature. Ralph enjoyed his schooldays and was keen on all forms of sport. His elder brother, Leslie, lived at home while studying for a degree in chemistry at University College London (UCL), and it was his accounts of the experiments that they were doing that excited Ralph and firmly set him on a course towards a career in science.
.In 1925, aged 16, Ralph passed the School Certificate with a sufficient number of subjects and distinctions to make him immediately eligible for university entrance. His father was in poor health at the time and it was decided that Ralph should go up to university rather than stay on at school for two more years to take the Higher School Certificate.