He was born on 1 May 1926, the only son of Walter Allinson and Alice Frances Cassidy of Tottenham, and educated at Friern Barnet Grammar School and Merton College, Oxford, matriculating in 1944. In 1951 he married Margaret Patricia Watts.
During his career, Allinson served as Principal at the British Ministry of Education (1948–58), First Secretary in Lahore and Karachi, Pakistan (1960–62), First Secretary in Madras and New Delhi, India (1963–66), Deputy High Commissioner, Nairobi, Kenya (1970–73), Deputy High Commissioner and Minister, New Delhi (1975–77), High Commissioner, Lusaka (Zambia) (1978–80) and High Commissioner in Kenya and Ambassador to UN Environment Programme (1982–86).
In recognition of his contributions to Her Majesty the Queen's Diplomatic Service, Allinson was awarded a knighthood—a KCVO—in 1979, having previously been awarded an MVO in 1961 and had a CMG conferred upon him in 1976.
- Levens, R.G.C., ed. (1964). Merton College Register 1900-1964. Oxford: Basil Blackwell. p. 345.
- "ALLINSON, Sir (Walter) Leonard". Who's Who 2016. A & C Black, an imprint of Bloomsbury Publishing plc; online edn, Oxford University Press. Retrieved 20 January 2016.
- "British Diplomatic Oral History Programme". Janus. Retrieved 20 January 2016.