I'm not sure if there is one "public," although when Her Majesty passes, perhaps people will feel united in grief across Great Britain or even the Commonwealth. I've been engaging penpals in Australia and England in conversation about the monarchy and am a little surprised (especially from the Australia) at the outright lack of interest. So it remains to be see how far the "public" response to Camilla goes (as someone upthread said, most people don't care about the royals). Just finished watching the 1990's documentary "London" where it was made to seem that the royals are not only ephemeral but perhaps beside-the-point for some English. I read several British papers daily and celebrities from America seem to get more press (even if it's not the DM).
But, if we consider ourselves here at the Royal Forums a kind of "public" (super-public?), then we can see that we have differing opinions about Camilla. I have to say that The Queen and Prince Philip have grown on me steadily as they've aged - their sheer intrepidness at carrying on with all they do has gained my interest and loyalty. I certainly didn't have much of an opinion QEII back in 1975, she was barely a presence on the world scene for me (so speaking as part of a "world public" now).
Like many people, I became more interested in British royals during the Diana years (stayed up all night to watch her wedding, knew many people who were completely disinterested in world events who did likewise, became disillusioned with Charles and his Camilla-affair as so many did, etc., etc.)
But in recent years, I've been very impressed with Charles's public speeches on the environment - and with Camilla's down-to-earth, steady presence in the lives of her husband, her stepchildren and her own children. She has come through some stormy times with her integrity intact and with a strong public image, I think (unlike Sarah Ferguson who keeps dropping bombs on her own toes).
It will be jarring to have any new monarch, and because we'll be going from seeing a Queen Regnant to a King with a Queen Consort, it's impossible for Camilla to in any way think about being a queen as HM has been a queen - she best just stay where she's been (behind and to the side of Charles). The public's perception of Camilla will be closely tied to the public's perception of Charles.
Is there a similar thread for Charles (can't remember)? I have no clue how to judge the public perception of Charles (worldwide) but I'd be very interested in a discussion of how he is perceived (and whether he's at all important) in the British public's mind.
Or from other Commonwealth members...