That seems pretty close to what I learned at school with the exception "I owe you five farthings". We were told that the tune was built from the sounds of the bells of each on the churches. So I assumed that it was the church at Old Bailey, not that I ever bother to find out if one exists. I am not sure whether St Clement's is St Clements Dane in the Strand or St Clement's of East Cheap. It's amazing how we accept these things as kids without thinking about them.

Then there is the game that is played to that tune which has the ending

Here comes the candle to light you to bed
and here comes the chopper to chop of your head

Chip, Chop, Chip, Chop, the last man's head.

I am sure that some one will come up with more accurate information.

TTFN, Bert.