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”.
Mrs May said, “I have been very clear that this government will make a success of our exit from the European Union. One of the ways we will do this is by embracing the opportunities to strike free trade deals with our partners across the globe.
“It is very encouraging that one of our closest international partners is already seeking to establish just such a deal. this shows that we can make Brexit work for Britain.”