I wrote to the restaurant before booking. Their response suggests that celiacs should avoid:
Hello Catherine, as you can see from the print on the gluten free part of our Menu, we clearly state that we are not a gluten free kitchen and, although we do our best to avoid cross contamination, we absolutely can’t guarantee that it wouldn’t happen.
Due to your severe condition, I respectfully suggest you find a more appropriate venue to visit.
Ciao, Chef Fausto Bellicini, Cuckoo’s GM
— Not very
— Some