Theresa May described the move as "very encouraging" and insisted it showed Brexit can work for Britain.
In a phone call to the new PM, her Australian counterpart Malcolm Turnbull said he urgently wanted to open up trading between the two countries.
Liam Fox, the new international trade secretary, said he was already "scoping about a dozen free trade deals".
But Britain cannot sign any deals while it is still an EU member.
Mrs May said: "I have been very clear that this government will make a success of our exit from the European Union.