This is the reason that we're not going to V&A when we visit in Dec. My husband is very picky and their menu is very limited. We have many upscale restaurants in our area and they normally accommodate his likes/dislikes, but my understanding that is that unless you're at the Chef's Table, you need to have an open mind (food-wise). He said that he wasn't interested... so we'll have many wonderful meals elsewhere...
But since it's your honeymoon, I would just call them and ask... You never know...
And to clarify - if you reserve the Chef's Table, they ask your preferences before they prepare your food. You're seated in a romantic enclave in the kitchen and your receive A LOT of personal attention from the Chef. That may be a good option for you.