He signed professional forms in September 1959, and made his first-team debut two years later, on 9 September 1961 at home to Colchester United, taking the place at left back of George Mulholland who was suffering from tonsillitis;[3] Darlington lost the match 2–0,[4] but Peverell stayed in the team for the next match, a League Cup visit to Rotherham United of the Second Division.
[7] He "thundered [the ball] in with his left foot from 30 yards (27 m)" for his first goal at the right end and the first in a 2–0 win against Hartlepools United on 28 March 1966 that took Darlington to within a point of the division leaders.
[8] He was ever-present as the team finished as runners-up – missing out on the title on goal average – and gained their first promotion since 1925.
[13] He made 419 league appearances for Darlington, 465 in all senior competitions, a total second only to Ron Greener's 490.
[14] He was described by the Northern Echo as "a no-nonsense right-back",[15] and by Neil Warnock, on whom he inflicted a ruptured spleen and fractured ankle during a match in 1972, as playing like a bouncer.