Green’s Dictionary of Slang

(bingo) the number four or, if the context makes this obvious, any combination ending in four.

1960		J. Franklyn Dict. Rhy. Sl.
1981		P. Wright Cockney Dialect and Sl. 109: 4 = knock at the door or door to door.
2002		B. Kirkpatrick Wicked Cockney Rhy. Sl.