According to this
https://en.wikipedia.org/wiki/St_Gregory_by_St_Paul%27s
it went up in smoke in 1666.
Yes I read that too! and I let it do my head in for about 20 minutes, but then I saw a wiki at Family Search and the parish name remained in use, which explains why I have baptisms post-1666.
I have added it as a category
https://www.wikitree.com/wiki/Category:City_of_London_Religious_Institutions
Thank you, I'll put some on right now.