What would it take to restore the prestige of the British monarchy?

Well the British monarchy (and the Australian monarchy which is legally separate, since you asked it in the Australia section) enjoys majority support, so not sure what you mean by prestige exactly. Royal families have always had scandals like any other group of people (they are all human, after all), but they reinvent themselves. The alternative would be a republic and even more politicians, but politicians never get themselves into scandals, right? lol

You are a dinosaur. The glory days of Rule Britannia are over and a good thing at that. Bullies, subjugators, oppressors, Just as we Americans, your rebellious offspring, became the world’s bullies after. Anything descended from the British Empire tends to be pretty screwed up, as in bigoted and racist, brutal to indigenous people. Your convict colony of Australia is the same way.

The British royals actually hire specialists whose job it is to keep the royals popular. After the disastrous times of Charles and Dianna's divorce, Princess Anne's divorce, Price Andrew's divorce, Prince Harry's partying and the scandal of him wearing a Nazi uniform to a fancy dress party, and the Rumours Prince Edward was gay (many wonder if his marriage was a sham to hide his being gay), Prince Charles marrying again to a person many disapproved of, and other royal scandals, the Royals apparently hired a Public Relations person to help them get back to being in the good books. We suddenly saw the young Royals behaving better and what appeared to be choreographed outings and charity work. Harry is patron to the disabled ex-military people and the Royals are taking on all sorts of patronage to charity groups. These days the Royals seem to be getting more respect and they are more mature and taking their royal duties very seriously.

Let the succession miss out Prince Charles.

What has the British monarchy to do with Australia? Our monarch is the Queen of Australia. That she is also the Queen of Canada, Jamaica. the UK and another dozen realms is completely irrelevant.

Their ratings are currently far higher than they've been for a while

Brexit is nothing to do with them; is there something else?

Once Muslims become the demographic majority in Britain the prestige of the new Caliph will not be questioned.

Who cares?? Every one of the family is a waste of space and the sooner all monarchies (particularly the British one) die out, the better.

nothinf