Walford began playing as a centre half. He started his footballing career at Tottenham Hotspur in 1974. At Spurs he made only two appearances before being signed in 1977 by Arsenal to play under former Spurs manager Terry Neill in a deal worth £25,000. Walford went on to play as a substitute in Arsenal's victorious 1979 FA Cup Final side. All in all he made 98 appearances and scored four goals for the Gunners altogether. In 1981, he moved to Norwich City for £175,000. Whilst with Norwich he helped the club avoid relegation and thereafter saw them being promoted to the First Division.