Green’s Dictionary of Slang

the vagina; thus by meton., sexual intercourse.

1937		R. Westerby Wide Boys Never Work (1938) 155: I bet they had the old Sir Berkeley all right. [Ibid.] 177: Mister Carden, who was in the habit of havin’ the old Sir Berkerley with Miss Thomas [etc.].
1938		J. Curtis They Drive by Night 23: That poor bastard Allen wasn’t never going to see a tart in bed again. [...] No more of the old Sir Berkeley for him.