I'm from the 'black country' in the midlands (uk) and my nan always used to sing me a version of this rhyme which is probably one specific to this region (we always seem to have our own versions!!)

I'm gonna go find the full thing from her but the joke was in the singing / saying of the lines by adding a 'H' where there isn't meant to be one. It started like this....

The dogs all had a party
They hired the (h)albert hall.
Each dame went with her sire
(h)And hung their (h)arseholes (h)on the wall.

Used to have me in tears, I'm sure it will again when she says it!!