MRCS LRCP 1944; MB BS Lond 1948, MD 1950, MS 1957; DRCOG 1949, MRCOG 1951.
Leverton was born in London on 7 May 1920. He was educated at St Bartholomew's Hospital, and also held travelling fellowships to USA and Europe. Leverton held junior appointments in London and Plymouth and served in the Royal Navy. In 1948 Leverton began to specialise in obstetrics at hospitals in Bristol and in 1952 was appointed obstetrical and gynaecological registrar at United Bristol Hospitals, where he was also tutor in obstetrics at the University. Leverton came to Manchester in 1953 when he was appointed senior registrar in obstetrics and gynaecology to the United Manchester Hospitals and St Mary's Hospitals. He was also on rotation to Withington Hospital and took part in undergraduate teaching. Leverton applied for the position of consultant obstetrician and gynaecologist at St Mary's Hospitals Manchester in 1958. He was a fellow of the Hunterian Society, a member of the North of England Obstetrical and Gynaecological Society and of MMS.