British Prime Minister Theresa May and her Australian counterpart, Malcolm Turnbull, on Monday promised to cooperate closely against terrorism and work towards a post-Brexit free-trade deal as soon as possible.
He later added the Liberal Party "stands for freedom or it stands for nothing", reports News Corp.
The Prime Minister said International Trade Secretary Liam Fox would visit Australia in the coming months as part of ongoing talks.
May said the topic came up during the recent G20 summit held in Hamburg, Germany and the two "discussed with our partners how we can step up worldwide efforts to increase pressure on Pyongyang, and find a peaceful solution to the ongoing threat North Korea poses to global security".
During a speech in London on Monday (UK time), Mr Turnbull highlighted the importance of the "sensible centre" - a phrase first used by his predecessor Tony Abbott - and went on to claim the LNP was "not conservative".
"It was essentially an anti-socialist party, it was a conservative party, that's now been abandoned under the tutelage of Malcolm Turnbull".
"The most vehement contemporary claimants are on the party's right wing".
Jeff Kennett has attacked Malcolm Turnbull for engaging in domestic politics while overseas.
Ag. President mourns `elder statesman' Maitama Sule
Shariff, said: "With a sorrowful heart, we announce the death of Alhaji Yusuf Maitama Sule, Danmasanin Kano this morning". The National Chairman of the Northern Elders Forum, Alhaji Maitama Sule is dead.
'We understand the USA concerns about the pressure that steel and aluminium sectors are under, ' he told ABC radio on Monday.
Mr Kennett said he had written a "laudatory" article praising Mr Turnbull's performance in his European trip but he was now in despair.
Turnbull said he was confident an agreement with Britain could be accomplished quickly once the United Kingdom leaves the bloc in 2019.
"What it's sent is a very strong message to conservatives in Australia [that] you're no longer welcome within the party of Menzies", Mr Bernardi told 7.30.
Meanwhile, former Liberal Premier of New South Wales, Nick Greiner compounded the criticism of former PM Abbott in saying that Abbott's "five point plan" to win the next federal election, which included plans to reform the Senate to make it easier for the governing party to pass legislation, was "never going to happen".
"My view is the public expects governments to govern", he said.
Opposition Leader Bill Shorten said Mr Turnbull was engaging in navel-gazing. "What everyone knows is this a government lacking leadership", he said.