Having seen Denmark, I think Margarethe got it right. In retrospect I think the Queen should have handed over earlier
I don't think that would have happened before the Platinum Jubilee.
But I think, had death not intervened, she would have made her last regnant act a request to Parliament to install Charles as Regent - either at the end of the summer at the time she would normally have returned to London, around the time of the Queen's Speech (if held in November) or in the Christmas Message.
If both Charles and William died or became too incapacitated to fulfil the constitutional roles of the monarch before 22 July 2031, then I think there will need to be a change to the Regency Act. Harry is already excluded because he lives overseas (yes he could move back, but I'm not sure that would be the right thing for him as his DC will surely be in school in California by that time, and he may well not want the disruption). Andrew - well, enough said, and also he's not a working Royal (a recent distinction with no standing in law, but I think a useful point in working out who).
I think a co_regency would be the best upshot, with Catherine in charge of the upbringing and education of the heir, and then Anne (depending on age/health) and/or Edward doing the constitutional part. In 2031, Edward will be 68, so only just over state pension age.