Verity was born in Headingley, an area of Leeds, on 18 May 1905. He was the eldest child of Hedley Verity, who worked for a local coal company, and Edith Elwick, a Sunday school teacher. Verity also had two sisters, Grace and Edith. The family moved to Armley, then to the more rural location of Rawdon. From an early age, Verity watched Yorkshire play County Cricket matches at Leeds, Bradford and, during family holidays, Scarborough. Later, at Yeadon and Guiseley Secondary School, Verity played school cricket, bowling left-arm medium-paced deliveries; he maintained this style until 1929 and was capable of bowling both inswingers and outswingers. Verity left school aged 14 to work for his father, who had established a coal business in Guiseley, and played cricket for Rawdon's second team. Success on the field persuaded Verity to seek a career in professional cricket and a place in the Yorkshire team. While working for his father, he devoted increasing amounts of time to cricket practice.