Mr Turnbull met in London with Metropolitan Police commissioner Cressida Dick - Scotland Yard's first female boss.
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 current UK threat level for international terrorism is "severe", meaning an attack is highly likely.
Mr Turnbull was later due to pay his respects to the victims of last month's London Bridge terrorist attack - two of whom were Australians - and meetBritish first responders to convey Australia's gratitude for their bravery and assistance.
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As well as dealing with a heightened terrorism alert level, the Met has 250 specialists investigating the fire at Grenfell Tower on June 14.
A total of 21 people who died have been formally identified by thecoroner and their families informed but there are fears for many others.
Terrorism and trade will be on the agenda when Mr Turnbull holds talks in Downing Street.
Mrs May, who went to Oxford University with the Australian primeminister, wants Britain to seize on the "opportunity" of Brexit to forge strongerties with its partners around the world.
"As the UK leaves the EU and forges a new role in the world, I am clear we should take the opportunity to strengthen our close partnership with Australia," she is expected to say.
She says Australia was the first country with whom the UK established a Trade Working Group following the Brexit vote.
"Discussions on an ambitious and comprehensive bilateral trade deal with Australia remain a priority for the UK."
The UK cannot legally negotiate trade agreements until after exiting the European Union but Mr Turnbull wants to move as quickly as possible to negotiate an agreement when that happens.
Trade Minister Steven Ciobo said the initial discussions had beenpositive and productive.
Mr Turnbull is also aiming to conclude an FTA with the EU by 2019.
The leaders will have a working lunch at Number 10 Downing Streetprepared by the Australian chef Skye Gyngell.
Before heading home, Mr Turnbull will also have an audience with the Queen.
On Monday night (London time) Mr Turnbull will deliver a speech on freedom in the context of national security and receive the Policy Exchange's 2017 Disraeli Prize.
