London: The last time Malcolm Turnbull spoke with the leader of what Australia would consider one of its closest allies, the verbal stoush that ensued ended up becoming a global story.

Mr Turnbull insists the call ended courteously, but his first phone conversation with President Trump was one of strong words as the men sparred over a refugee-swap deal brokered under the former Obama administration.

But on Wednesday, Mr Turnbull heard a gentler sound on the other end of the line when he spoke to the other best friend of Australia - Britain's Prime Minister Theresa May.

Mrs May is keen to recast her country as "Global Britain" as it negotiates its exit from the European Union and strikes free trade deals, including with Australia.

Mr Turnbull told Mrs May Australia wants to maintain its close relationship with the United Kingdom as Britain Brexits.

Both leaders said they "looked forward to holding preliminary conversations on a comprehensive bilateral free trade agreement in due course."

They also discussed the Middle East and the two countries' contributions to fighting Islamic State. Iraqi forces are making significant advances in Mosul, Islamic State's last stronghold in Iraq.

A 10 Downing spokeswoman said the leaders agreed on the need to create conditions for the stability of Iraq once Mosul falls.

Critically, Mrs May underlined the need for a transition in neighbouring Syria away from President Bashar al-Assad.

In previous weeks, UK Foreign Secretary Boris Johnson has openly mused about whether Britain could accept Mr Assad continuing to preside over Syria. However he later hardened his position following the release of an Amnesty report detailing claims the regime killed up to 13,000 people in a series of mass hangings.

Mr Johnson met Foreign Minister Julie Bishop in London on Thursday.

In a statement, the minister said a future free trade agreement would grow the two countries two-way trade valued at $27 billion in 2015/16.

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