It's not advisable to not vaccinate British Shorthairs. Core feline vaccines prevent diseases that can be fatal to cats. Even cats kept indoors can become infected if their owners carry pathogens. If a cat contracts diseases like feline panleukopenia or bronchitis, the owner will not only incur significant financial and time costs, but these diseases also have extremely high mortality rates. Therefore, vaccinating your cat is essential for its safety.
Even owners can bring germs home. Homes generally need regular ventilation by opening doors and windows, meaning they aren't completely sealed off. The flow of outside air increases the likelihood of various bacteria and viruses entering the house. Owners can also bring germs home from contact with sick cats or objects. Therefore, cats indoors aren't 100% protected from illness. There's a significant chance they'll bring in germs from outside, which can then infect and cause disease. That's why even cats that never go outside need to be vaccinated.
