From my school (and rugby playing) days, there were many other verses. Although no suited to mixed company!

She stood on the bridge at midnight,
Flicking snot-balls at the moon.
She said "Sir, I've never had it"
But she spoke too f****** soon.

She stood on the bridge at midnight
Youthful face, and chest quite flat.
She was quite the winsome virgin.
But I soon took care of that.

We also reversed two lines of the chorus:

"It's the same the whole world over.
It's the rich that gets the pleasure.
It's the poor that gets the blame.
Ain't it all a bleeding shame?"

It seemed to scan better!

Cheers

Nigel