The leaders, who have known each other since their Oxford University days, walked through the market, talking to stall holders about the devastating event.
"By fighting terrorism - with proportionate means - we are defending liberal values", he will say.
Turnbull praised the "decisive action" of police in shooting dead the three attackers who, wearing fake suicide vests, had rammed pedestrians on London Bridge and then stabbed people at the nearby market.
Boden, one of two Australian women who died, was killed after she rushed to help victims while the attack was still unfolding.
After a brief chat, he said: "Thank you so much for everything you have done".
Mr Turnbull said meeting two of the officers who responded to the incident was very emotional.
Mr Turnbull successfully convinced G20 members at the Hamburg summit to include in a statement on terrorism support for companies to provide access to encrypted communications where necessary.
Malcolm Turnbull talks terror, trade with UK PM Theresa May
Commissioner Dick took on the role on April 10, with her first official engagement being the funeral of PC Keith Palmer, the officer killed in the Westminster attack.
"The lesson is clear: weak borders fragment social cohesion, drain public revenue, raise community concerns about national security, and ultimately undermine the consensus required to sustain high levels of immigration and multiculturalism", he will say.
At a joint media conference, the two leaders talked up the potential for an Australia-Britain free trade agreement which Mr Turnbull said would be concluded quickly.
"This office will provide a collaboration space for the Naval Group and Lockheed Martin Australia to work closely with our Australian government partners to provide the best possible submarine fleet to provide protection for Australia's trade and assure the nation's maritime security", said Vince Di Pietro, CEO of Lockheed Martin Australia and New Zealand.
Turnbull said he hoped the European Union deal could be finalised before the expected date of Brexit in March 2019.
Although the United Kingdom is unable to complete its own trade deals before leaving the European Union in March 2019, ministers are able to lay the groundwork for an agreement, with Liam Fox, the trade secretary, planning to visit Australia for preliminary talks in the coming months.
Domestic politics will be on the prime minister's mind later on Monday when he delivers a speech the Policy Exchange, where he will also receive the think tank's Disraeli prize.
Mr Turnbull will also meet with Queen Elizabeth II during his visit.