An "ambitious" trade deal between Australia and the UK will be a key item on the agenda today when Malcolm Turnbull makes his first official visit to Downing Street as Prime Minister.

Following Hamburg's G20 summit and a stopover in France to meet with French President Emmanuel Macron, Mr Turnbull has arrived in London for meetings with the British Prime Minister Theresa May and Her Majesty the Queen.

National security, counter terrorism and trade are set to dominate today's talks after the two leaders visit the Borough Markets to pay respects to the victims of the recent London terror attacks, including two Australians.

Ahead of today's closed-door meeting, Ms May said the UK would "seize the opportunity" of Brexit to forge closer ties with Australia.

“I am clear that discussions on an ambitious and comprehensive bilateral trade deal with Australia remain a priority for the UK," Ms May said.

"We have both made clear our intention to continue to deepen our trade and investment relationship as the UK leaves the EU."

Camera Icon British Prime Minister Theresa May and Australian Prime Minister Malcom Turnbull during the G20 summit in Hamburg. Credit: Matt Cardy/Getty Images

Praising the "close partnership" between Australia and the UK, Ms May is also expected to say today that the recent terror attacks serve as a reminder of the need to pursue stronger cooperation on security matters.

“At times such as this we are reminded of the importance of the strong ties that have bound our two nations together for over a hundred years," Ms May will say.

“And we will continue to stand together as close allies and firm friends against those who want to destroy our precious values and our way of life."

Following a commitment at the G20 summit to do more to police terror activities online- an issue pushed at the summit by Mr Turnbull - Ms May will also add her voice to the call to tackle "the spread of Daesh’s (Islamic State) hateful ideology online."

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“Alongside this, our national cyber security centres cooperate closely to crack down on malicious cyber activity," she will say.

"Our law enforcement agencies work together to tackle serious and organised crime – particularly the illegal financial flows that fund criminal gangs and terrorists. And our intelligence sharing partnership under the Five Eyes alliance is central to our efforts to tackle the shared threats we face.”

Mr Turnbull is also expected to meet other senior ministers and security agencies during his visit.