It wouldn't be the first vegetarian restaurant in the world. There used to be a nice one in Deptford but it closed years ago. There is certainly a gap in the market for a quality vegetarian restaurant and I'm sure they wouldn't exclude meat eaters.
There is no need to eat meat every time you go out for a meal, in fact I almost never do. Good vegetarian food can often be almost as nice as a decent piece of well cooked meat.