I only ever once encountered "cock" in the meaning of female genitalia in a rhyme I learned aged about 8 or 9 in northern England in the mid/late 50's:

Put a penny in the slot
See what Betty Grable's got
Two big tita and a hairy cock
That's what Betty Grable's got

I thought it must have been a mistake by the people I learned it from, and they must have meant "twat" not "cock", but maybe not.