The BBFC (British Board of Film Classification) is responsible for classifying films in the UK using a rating system of U, PG, 12, 12A, 15, and 18. Films are classified based on their content related to strong language, violence, imitable behavior, drugs, horror, nudity, and themes. The document discusses a hypothetical film being submitted to the BBFC for classification that contains strong language, violence, imitable behavior involving drugs and hitting someone, depictions of drug use, scary kidnappers, and crime/drug related themes, leading to the conclusion that it should receive an 18 rating as not suitable for those under 18.