Conversation:

I found another site which quotes a full version of the rhyme and also identifies all the churches; there is an extra couplet in it, viz. "You owe me ten shillings say the bells of St Helens"
http://www.rhymes.org.uk/oranges_and_lemons.htm

Point of information re contending churches :
Surely this rhyme is about bells and churches in the City of London (London Town). Neither St Martin-in-the-Fields nor St Clement Danes is or has ever been in the City of London. I know that Whitechapel and Stepney are both outside the City, but in olden times the City spread to the East and not to the West, and I suspect that those places were considered as suburbs in exactly the way that Westminster was not.

Thanks for reading the entry! It's nice to know that all this time after I wrote it, people are still reading.

The City of London has never really spread past the Tower, as that was the limit of the City Wall - A2266832 - and it's always simply been the swuare mile. I suppose that depends on what you mean by 'olden' times, and what you mean by spread though.