Well, no. In the last few weeks, prompted by this event, there's been no shortage of op-eds in the British media on the continuing significance of the monarchy, pro- or anti-. I'd be willing to place a bet that 'subject' (either the word itself or the concept) doesn't appear in any of them. It's simply not an issue here.
It does seem to be an issue when Americans talk about the monarchy, presumably an (entirely reasonable) legacy of what is taught in schools about the events of the 1770s.
See, I told you I get any of it. lol