Since the creation of The Football League, Tottenham Hotspur is the only non-league "giant-killer" to win the Cup, taking the 1901 FA Cup with a victory over reigning league runners-up Sheffield United: although at that time, there were only two divisions and 36 clubs in the Football League, and Spurs were champions of the next lowest football tier - the Southern League and probably already good enough for the First Division (as was shown when they joined the Second Division in 1908 and immediately won promotion to the First.
How many clubs where in the football league? 
36 clubs in the Football League