Many thanks for your help – yes, John Dippa does look very likely! That's one alternative spelling I hadn't thought of. The IGI is usually pretty good at coming up with near (and sometimes not so near) matches, but it certainly missed that one. I didn't know you could use parents' first names only with a batch number – that'll be useful in the future.
As you say, Francis remains a mystery. I don't know when James was born, but in his will signed shortly before his death in 1771 he leaves an annuity to his mother; if she was still alive I imagine he can't have been more than around 60 years old. Possibly time enough to have had an earlier marriage and son, though in his will he makes no mention of him (he doesn't make any mention of John, either, though he does name James and Ann). He leaves his goldsmith's business in trust to his brothers-in-law, directing them to carry on his trade (as they were a pastry cook and a plumber they might have found that difficult!) and give the profits from it to his mother, wife and children. So I wonder why he didn't mention this Francis Duppa, whoever he was?
Oh well, just one more family mystery to tease and torment us! But thanks for finding John for me.
Jane