William I was known as 'The Bastard', as he was the illegitimate son of Duke Robert I of Normandy, and Herleve (also known as Arlette), daughter of a tanner in Falaise.

He wasn't known for having a big todger.

We've never had a 'Queen Hortense' either, so I reckon this song is just a bit of fun. If Kipling really did write it, then no wonder the King isn't named - he'd have lorst 'is bleedin' 'ead. And quite right too.