During his career, Cundy played for Chelsea (1988-92, 41 league appearances), Tottenham Hotspur (loan in 1992, 1992 - November 96, with 28 games), Crystal Palace (one month-loan, 1995), Bristol City (another 30-day loan, 1996), Ipswich Town (after a loan, November 1996-99) and Portsmouth.
He also made a TV appearance on the British food programme Ready Steady Cook alongside fellow footballer Graeme Le Saux.