Monkhouse was born on 1 June 1928 at 168 Bromley Road, Beckenham, Kent, the son of chartered accountant Wilfred Adrian Monkhouse (1894–1957) and Dorothy Muriel Monkhouse "née" Hansard (1895–1971). Monkhouse had an elder brother, John, who was born in 1922. Monkhouse's grandfather John Monkhouse (1862–1938) was a prosperous Methodist businessman who co-founded Monk and Glass, which made custard powder and jelly. In a 2015 documentary, it was revealed that Monkhouse and his older brother suffered from physical and verbal abuse by their mother.