There is a George Cooper, son of Christopher and Mary, baptised 14 Feb 1791 at St Giles in the Fields, but the baptism record doesn't give any extra info to confirm it is the right George. From Googling, your Christopher Cooper was a grocer of 67 New Compton Street. I did find a British History Online page which says that New Compton Street was in St Giles in the Fields (footnote no 1):
https://www.british-history.ac.uk/su...33-4/pp193-201