I can’t answer about the OP’s rabbi, but the rabbonim in my town certainly enforce tznius halachos with the rabbim no less than they enforce kashrus halachos, shatnes halachos and Shabbos halachos.
zahavasdad: Actually that isn’t yet true. The proposed law only becomes effective once all British Commonwealth nations ratify it into law, something that has yet to occur. Otherwise what could happen is that the different Commonwealth nations could have different Monarchs.