@tamsin I don't have coeliac but I work with disabled university students in England. coeliac students often need their own kitchen space for gluten-free reasons.
One coeliac student told me that at one point she was getting gluten poisoning from a certified product - I think a type of breakfast cereal which she ate a LOT of because she'd been deprived since diagnosis.
Can you get some dietician advice about the foods your household is buying to identify if anything is still glutenny?