Green’s Dictionary of Slang

billy n.2

[? a play on the billycock hat, which is ‘felt’]

the vagina.

[UK] ‘Gently Johnny my Jingaloo’ in Speaight Bawdy Songs (1975) 8: I put my hand all on her thigh / She says to me do you want to try? / I put my hand all on her billy.