Wright was only 18 when he arrived at the Dell and the Saints were flying high at the top of the table under manager Lawrie McMenemy. He made his debut for the club in a 3–1 win over Leeds United at Elland Road on 17 April 1982, a game which saw two Saints legends, Kevin Keegan and David Armstrong, score the goals. He featured in two of the Saints' remaining five league matches that season as Southampton eventually finished seventh in the league and qualified for the UEFA Cup.