Hi DS2 has wheat/dairy allergy. We've been to Center Parcs a few times, but not impressed with their approach to catering for allergies.
We go to Sherwood Forest, and now tend to go out for breakfast at Chez Pierre (DS2 has bacon, eggs and beans), then take food with us for other meals.
Huckleberry's offered to provide things like spare ribs without sauce, or plain chicken breast, but we tried that, and they were a bit dried up and unpleasant - and the chips had a wheat coating, which we only discovered when they arrived. We had previously been told they were fine!
They did do plain fish and boiled potatoes once, with butter-free veg and that was nice - but it is an expensive place to eat IMO.
The supermarket is expensive and does not provide any specific wheat products, so take your own.
It might be slightly easier for your family, as we have the added problem of DS2s dairy allergy too, so it is well worth emailing them and asking what they can provide.
It's about time they started providing food for all their guests - it's not much of a holiday for us Mums otherwise!