It must be Saint Clements Dane in the Strand, because it plays Oranges and Lemons from the steeple. I have no idea if there was ever a market in the area. It was Samuel Johnson's home parish for quite a while and his statue stands outside.

Aren't the lyrics in Mother Goose? I don't have a copy to hand but you mothers and fathers out there can check. That might be the making of another thread. My mother used to sing to me almost every rhyme in there (and in Alice in Wonderland and Through the Looking Glass) which she had presumably learned from her mother, a Londoner. I wonder if anyone has ever recorded the whole set. She never did sing Old Grimes Is Dead and I've often wondered what the tune to it is.