Green’s Dictionary of Slang

(bingo) the number ten.

1943		M. Harrison Reported Safe Arrival 85: ‘Ten’ is [...] ‘Shiny Ten,’ or ‘Downing Street’.
1960		A. Burgess Doctor Is Sick (1972) 197: The flop-tied man dismissed two little ducks, legs eleven, doctor’s chum, Dowing Street, Kelly’s eye, and various others.
1981		P. Wright Cockney Dialect and Sl. 109: 10 = cock(s) an’ ’en (otherwise Dahnin’ Street).
2001		J. Burkardt ‘The Bingo Code’ 🌐 10: Downing Street.
2002		A. Aziz American Diary 108: ‘1 and 0, number ten Downing Street, — ’ ‘Bingo,’ I saw Bakhtwar raising his hand. He got an electric iron as prize.