Malcolm Turnbull's meeting with Queen Elizabeth II was almost very awkward.

Staunch republican Malcolm Turnbull says 20 years ago he would have never imagined that he would meet the Queen as Prime Minister of Australia.

The final official event for Mr Turnbull before heading back to Australia after a trip to Germany, France and England was an audience with the Queen at Buckingham Palace.

Speaking to reporters before the meeting, Mr Turnbull, who co-founded the Australian Republican Movement, said politics is “full of unpredictable events” before cleverly declaring himself an “Elizabethan”.

“Even republicans like myself can be, and in my case are, very strong Elizabethans,” he said.

The Prime Minister paid tribute to the 91-year-old monarch as having embodied “selfless public service, dignity, wisdom and leadership for longer and more magnificently than anyone alive today”.

The Queen wore a diamond-encrusted wattle brooch while receiving Mr Turnbull on Tuesday.

The Queen has worn the yellow and blue diamond item many times, which was given to her early in her reign during the 1954 Commonwealth tour.

The monarch has been invited to open the Commonwealth Games on the Gold Coast in 2018.

Asked whether he expected confirmation of which royal might attend, Mr Turnbull said: "I may be better informed this afternoon."

Mr Turnbull has publicly advocated for a republic, but believes such a change would not be supported by Australians during the Queen's reign.

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 called on the the Prime Minister to 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.

Mr Turnbull had breakfast with UK corporate chiefs where they discussed greater investment in Australia.

Listen: Mia Freedman talks to Malcolm Turnbull about life as the PM of Australia. Post continues... 

He then met with university representatives to discuss ways to link researchers with industry and address fears that Brexit could have an impact on innovative business.

Mr Turnbull said "a lot of people" were downcast about the Brexit decision and thought it was a mistake.

"But British people should see this from an optimistic point of view. They should be able to say, 'We've made that decision, we are part of a global economy and we should embrace it' - and Australia will be part of it."