British republicans say they are "disappointed" Australian Prime Minister Malcolm Turnbull did not try to stop the Prince of Wales from being anointed as the next head of the Commonwealth.

At a Commonwealth leaders "retreat" in the grandeur of the Queen's home, Windsor Castle, it was agreed Prince Charles would become the next symbolic leader of the 53-nation club.

During the opening of the biennial Commonwealth Heads of Government Meeting (CHOGM) at Buckingham Palace on Thursday, the Queen declared it was her "sincere wish" her son eventually get the non-hereditary role.

Sorry, this video has expired The Queen backs Prince Charles as head of the Commonwealth

But UK organisation Republic's chief executive Graham Smith said the Queen's call amounted to "nepotism".

"It's a shame the one time the Queen makes a rare, unprecedented comment, it's about pushing the interests of her own son," he said.

"This is a really rare, missed opportunity to do something decisive to make the Commonwealth more relevant, more representative in the long-run and have a different kind of figurehead."

The Republican movement in Britain is not as well-supported or as high-profile as it is in Australia.

Campaigners in the UK want to get rid of the Royal family entirely.

It was agreed Prince Charles will become the next symbolic leader of the 53-nation club. ( AP: Matt Dunham )

But most opinion polls suggest the monarchy remains relatively popular and many Britons are excited about the imminent arrival of a new Royal baby, as well as the marriage of Prince Harry and his American bride-to-be Meghan Markle.

Some British republicans had hoped Mr Turnbull, a well-known high-profile advocate of installing an Australian head of state, would campaign against a Royal being put in the head of Commonwealth role.

"No-one would have been surprised, no-one would have been upset — with the possible exception of some of his own backbench," Mr Smith said.

"We can only guess that's the reason or there has been some hard-nosed horse-trading behind the scenes that we don't know about.

"This is another feather [in the Royal family's] cap."

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Australia signalled its preference for Prince Charles to become the next head of the Commonwealth when Julia Gillard was prime minister five years ago.

This week, Mr Turnbull again restated his view the "monarch of the United Kingdom" should hold the role — though he said there was no inconsistency in being an Australian republican, while also supporting the British Royal family playing a symbolic Commonwealth leadership role.

Australian Republican Movement chair Peter FitzSimons said he did not understand why Mr Turnbull backed Prince Charles as the next head of the Commonwealth.

"Malcolm Turnbull is, I assure you the most passionate Republican in the country while Christopher Pyne remains the most eloquent, but I don't quite get why the Prime Minister is backing a system whereby a future monarch rises by birth right alone," he said.

He said the "ascension" of Prince Charles to the role showed the system was outdated.

As CHOGM wrapped up overnight, UK Prime Minister Theresa May praised the Queen for her work over the decades and said it was "fitting" Prince Charles would succeed his mother due to his backing of the Commonwealth "for more than four decades".

Commonwealth leaders also agreed to try to protect the world's oceans from pollution and climate change, and committed themselves to a "cyber-declaration" to combat digital crime.