Via our website came a query from a retailer so frustrated by a customer who is trying to get double yellow lines painted outside his shop that he wondered if he could ban her. He writes: "We just don't want to serve her so that she can feel what so many people would feel if we were forced to close. Can I do this?"
The answer is that you are perfectly entitled to ban anyone you like. Your store is private property so there is an implied invitation to customers to enter and shop. In this case, our reader will be uninviting her.
Trading Standards, I'm sure, would recommend that you write to her with the information - but, of course, this would mean that you would need her address.