After spells as an amateur with Colwyn Bay, Skelmersdale United and Wycombe Wanderers, Suddaby began his professional career with Blackpool in 1970, and went on to make over 300 league appearances in a decade at the club.
He made his debut for Blackpool on 23 January 1971, in a defeat at West Ham United in the fourth round of the FA Cup.
He scored two goals – against Leyton Orient in a 4–1 victory at Bloomfield Road on 9 October 1971, and in a 5–0 whitewash of Watford, also at home, on New Year's Day.
Suddaby's final season at Blackpool, 1979–80, saw him start in fifteen of the first sixteen league games, before he was sold to Brighton & Hove Albion in November 1979.
After 23 league games for Brighton, Suddaby had a short stint at Wimbledon, before returning to Wycombe Wanderers in 1982 for his final spell as a player.