Here is the oldest version of "Craven A" that I have yet found.  It is from the 4th printing of the 1956 book titled Count Palmiro Vicarion's Book of Bawdy Ballads
 

LITTLE JIM

Now here's a pretty little song so listen if you will
About a little fellow born on night on Tooting Hill,
He was Born on Tooting Hill my boys, but spawned in Camberwell,
And when he popped out he gave a shout: "My Old Man fucked her well!"

Little Jim, content with masturbation,
Little Jim, playing with his tool,
Little Jim, content with simple frigging,
Thought a cunt was something you were called at public school,

Now down a Egham Manor there was a great ado,
For he buggered all the prefects and all the masters too,
But finally he was expelled or so the records say,
For tossing off the Prince of Hales on Coronation Day.

Now Jenny was a whore in good old Cambridge town,
Who had gamahuched the Proctor while he wore his cap and gown;
SO his Uncle wrote to Jimmy saying "Quick, and pack your things,
For the cunting seasons opens at the Twelfth at Kings!"

His arrival at the 'Varsity was really quite grotesque,
For he laid his penis down upon his tutor's desk;
Said his tutor, "If the beastly thing drops off at an early date
Please send it.  I should like it as a special paperweight."

Then he went to live with Milly where he began to find
That all his pals were queuing up of what they called a "grind,"
So down beneath the bed he lay despite the awful smell,
And every time a client came, young Jimmy came as well.

And Milly's all a landlord's daughter will or ought to be,
She rubs her Aunt each morning while she drinks a coup of tea;
He's been through her so many times, the magistrate declares,
That her vagina constitutes a legal thoroughfare.

Note: This text is from Count Palmiro Vicarion's Book of Bawdy Ballads (1956. Fourth printing 1962).  Unpaginated. Song XXIX.