I've dined solo at V&A several times. I really enjoy it. The staff takes extra time with solo diners. If you have eaten solo at a sit down before, I'm sure you will enjoy it. I wouldn't recommend it as someone's first solo meal. I really enjoy food and love savoring every morsel. Ask for Nancy as your server, she'll make you feel very comfortable.
You might want to look at the "Adult and Solo Traveler" forum. If you post additional information, such as the date, you might find someone going solo at the same time who might want to do V&A with you. They will do separate checks if you ask. Then you will at least have one (or more) to talk to during the meal. If you find them on disBoards you will have at least one subject to talk about.