Close was born into a working class family in Rawdon, West Riding of Yorkshire, around west of Leeds, on 24 February 1931. His parents were Harry, a weaver, and Esther ("née" Barrett). He was the second eldest of five boys and a girl. The family lived in a series of small council houses in Rawdon, Guiseley and Yeadon. Growing up, Close practised cricket with his father in the houses' back gardens; Harry Close was himself a keen cricketer, who kept wicket and was a big hitter in the Bradford Cricket League, although he never attained the standard of the Yorkshire county team. Rawdon had cricketing pedigree: Hedley Verity—an England international in the period before the Second World War—grew up there, and the Verity family continued to live in the village. At Rawdon Littlemoor Primary School, Close was taught by Grace Verity, Hedley's sister, and he was friends with two of his children, Wilfred and Douglas.