Turnbull: Australia 'very keen' for trade deal with UK
He said a UK agreement could follow swiftly: "My government's position is very simply this: economic prosperity has been demonstrated to be delivered by free trade and open markets - that is one of the major reasons why Australia has had 26 years of uninterrupted economic growth."
He said Mrs May's vision for post-Brexit Britain "is one filled with optimism". "It's not a counsel of despair as some people have said."
Turning to the PM, he added: "I know Theresa that you believe passionately that the British people can do anything, can achieve anything and that your post-Brexit Britain will be a Britain with big horizons, big opportunities, free trade, open markets.
"You're right, that is the future. That's where our prosperity has been delivered and I know that it's where your prosperity will come."
Mrs May said a trade deal with Australia was a "priority" for the UK after Brexit, to expand on the ?14bn-worth of trade between the two nations.
"We've both made clear our intention to continue to deepen our trade and investment relationship as the UK leaves the EU," she said.
"Our Brexit negotiations have started well, and I have made clear to prime minister Turnbull that an ambitious and comprehensive bilateral trade deal with Australia remains a priority for the UK."
Earlier, the two prime ministers - who were at Oxford University at the same time - visited the scene of the Borough Market atrocity to be briefed by police officers and paramedics who rushed to the aid of victims and survivors.
They also spoke to traders in the market, one of London's most popular visitor attractions.
The two earlier met Church leaders at nearby Southwark Cathedral, including the Reverend Canon Michael Rawson, the Sub Dean of the cathedral.
The UK and Australia have strong commercial, cultural and security links through the Commonwealth and the "five eyes" intelligence alliance.
Although the UK cannot negotiate trade deals with other countries until after Brexit, Australia is one of the countries with which Whitehall officials have set up a working party to look at the issues involved.
International Trade Secretary Liam Fox will be travelling to Australia in the coming months.
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