Old Bailey was not a church, but I think the rest of them are.I suspect that the rhyme is older than Wren, who did most of his work on London churches after the Great Fire in 1666. (The present St. Clements Dane is for the most part a reconstruction dating from the 1950's, the church having been hit by incendiary bombs during WWII) I suspect that most of the rhymes in Mother Goose predate 1666, and were collected later.
What does this annotated version say on the subject? I am also curious to know if the tunes to which the rhymes are set are original, or if they were concocted later. There are of course different versions of Mother Goose, some of which have altered to suit politically correct tastes.