Malcolm Turnbull is being urged to raise with the Queen how she might assist Australia transition to a republic.
Mr Turnbull, who co-founded the Australian Republican Movement, has publicly stated he would like to see an Australian as head of state but such a change would not be supported during the Queen's reign.
His Buckingham Palace meeting with the monarch late Tuesday (AEST) will be the final formal event for the prime minister before heading home, having attended the G20 summit in Hamburg, talks with French President Emmanuel Macron in Paris and events in London with British Prime Minister Theresa May.
Ahead of the audience, Mr Turnbull said the Queen embodied selfless service, dignity and leadership.
"Even republicans like myself can be and in my case are Elizabethans," he said.
ARM is pressing for a national vote in 2020 on whether people want an Australian head of state and how one should be chosen.
This would be followed by a full referendum in 2022 to change the constitution.
Mr Turnbull said in a speech in December his preferred model was an advisory plebiscite offering a choice between two republican models - most likely direct election and parliamentary appointment.
Once the model is chosen at the plebiscite, the parliament would formulate the terms of the amendment in line with the people's choice and present it at a referendum.
ARM said the prime minister should make clear to the Queen Australia would still be a commonwealth country if Australians vote to become a republic.
Labor, meanwhile, wants Mr Turnbull to ask the Queen how she might help Australia transition to a republic.
"But I've got no real hope that he's going to do that," frontbencher Mark Dreyfus told ABC radio on Tuesday night.
Mr Dreyfus said he was disappointed Mr Turnbull was not doing anything to bring about an Australian republic but hoped there was enough common ground between the major parties to forge a bipartision position.
"Malcolm Turnbull's the man that said John Howard broke the nation's heart in 1999 but we've seen precious little of that republican spirit from Malcolm Turnbull since he became prime minister," he said.
"I'm remaining hopeful he can return to this subject."
Mr Turnbull will meet with business leaders to discuss trade and investment, as well as hold a roundtable discussion on education and innovation.
Quizzed at a Policy Exchange function in London on Monday night, Mr Turnbull said he wanted to conclude a free trade deal with the European Union before achieving a bilateral deal with a post-Brexit UK.
The prime minister wants the EU deal completed by 2019 and has the support of President Macron and German Chancellor Angela Merkel to do so.
