We dined at the Chef's Table for our 23rd anniversary and it was great. You're seated in an alcove next to the kitchen. Scott Hummel, the chef, comes over to share a toast with you and to discuss any likes/dislikes/allergies with you. You then have about a zillion courses. Seriously, I don't even remember how many we had but they were each wonderful and beautifully presented. You have a chance to ask questions of the cooks working near you. It was a great time.
However if you've never dined at V&A before, you might also consider celebrating in the main dining room. It is an intimate, romantic room.