MB ChB Manch 1951, MD 1958; FRCP 1972.
Leeming was born in Salford on 13 September 1927, the son of James Pensam Leeming, a dental surgeon. His aunt, Marianne Peach, was a skin specialist. Leeming was educated at Manchester Grammar School and the University of Manchester. He held junior appointments in Manchester at MRI, the Northern Hospital and Crumpsall Hospital. In 1958 Leeming was a registrar fellow in chronic illness at the Johns Hopkins Hospital, Baltimore, returning to MRI in the following year.
In 1962 Leeming was appointed senior registrar in geriatric medicine at Crumpsall Hospital, and from 1963 to 1967 he was consultant physician in geriatric medicine for Bolton and District Hospitals. From 1967 Leeming was consultant physician in the department of geriatric medicine at South the University of Manchester Hospital, and in 1968 became honorary lecturer in geriatric medicine at the University of Manchester. Leeming was a member of the British Geriatrics Society, British Society for Research on Ageing, British Society for Social and Behavioural Gerontology, and MMS.