Mr Turnbull, who received an intelligence and security briefing in London on Monday, told reporters at a joint media conference with British leader Theresa May later he was "always interested in learning about the British experience".
"This is no place for set and forget," he said.
"We have to be dynamic, agile constantly asking can we improve the way our agencies are keeping Australians safe."
Integrating departments such as attorney-general, Australian Federal Police, ASIO, Australian Border Force and immigration has been resisted by some cabinet ministers.
North Korea
Mr Turnbull and Ms May say China is the one country that has the ability to "bring the North Korean regime to its senses" and stop its nuclear missile program.
The two prime ministers told reporters their aim was the denuclearisation of North Korea.
Ms May said the UK had the same approach as Australia and believed China "was the country with the greatest possible leverage on North Korea".
She said that was the message she had given to Chinese President Xi Jinping at the recent G20 summit in Hamburg.
Mr Turnbull said China had the ability "to impose huge economic pressure on North Korea, and they should do so".
He said China was the only country that could "bring the North Korean regime to its senses without some form of military intervention".
North Korea's recent successful test firing of what is believed to an intercontinental ballistic missile has heightened global tensions over the regime's weapons program.
Free trade
The pair also expressed expressed the desire to forge a free trade deal as soon as legally possible.
“We move quickly. Australians are fleet of foot. We don’t muck around and we’re very simple. So we move as quickly as the UK is able to move,” Mr Turnbull said.
“We are absolutely signed up for free trade, open markets. It’s been key to our continued run of economic success,” Mr Turnbull said.
Ms May highlighted the trade links are worth close to $18.03 billion.
“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 said.
Australian Republican Movement
The Australian Republican Movement has called on Mr Turnbull to reassure the Queen the nation would remain in the commonwealth should it become a republic in coming years.
The prime minister is due to have an audience with the Queen at Buckingham Palace on Tuesday, before he returns to Australia.
"The prime minister should make clear that Australia will still be a commonwealth country if Australians vote to become a republic at some future date - whether during the Queen's reign or after it," ARM said in a statement.
When the Commonwealth Games comes to Queensland in 2018, there will be more than 30 republics competing, including India, South Africa, Singapore and Samoa.
ARM is pressing for a national vote in 2020 for Australians on whether people want an Australian head of state and how an Australian head of state should be chosen.
Borough Market visit
Mr Turnbull and Ms May have met Australian ambulance officers and British police who responded to last month's terror attack in London.
The prime ministers visited Borough Market on Monday, with Mr Turnbull on behalf of Australians thanking the "very brave" police officers who tried to save people, including two young Australian women, who died that night.
UK Prime Minister Theresa May and Prime Minister Malcolm Turnbull walk through Borough market in London. Source: AAP
The leaders, who have known each other since their Oxford University days, walked through the market, talking to stall holders about the devastating event.
One stall holder booed Ms May as she walked past, saying "they don't care about us".
But others were more positive, relating their stories of how terrified people reacted.
As they stood just near where the terrorists were shot dead, some of the vendors described how terrified people reacted.
