UK offered Brexit free trade deal with Australia
Australia has called for a free trade deal with Britain following its exit from the European Union.
Theresa May described the move as "very encouraging" and insisted it showed Brexit could 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 the UK cannot sign any deals while it is still an EU member - and experts warned trade deals take a long time to negotiate.
- Live updates: Sunday politics
- May's cabinet: Who's in, who's out?
- What happens next: May's to-do list
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," she added.
Economist Howard Archer told the BBC News Website that post-Brexit the UK would be looking to trade with other parts of the world outside of the EU.
"That is something that the Leave campaign was pushing for, so that we would be open to other deals with other countries and regions," he said.
He said trade deals "take a very long time" to be drawn up, and that while there might be a desire for the UK to seek out as many agreements as possible, there should be a focus on the most important trading partners.
Equally important, the UK should also look for major deals that can be quickly concluded and not drag on for years, said Mr Archer, chief UK and Europe economist at IHS Global Insight.
"There has been a focus recently on how few trade negotiators we actually have got in the UK at the moment," he added.
"So a trade negotiator working on a deal with Australia would not then be available to work on a trade deal with China. It means decisions have be taken about which deals to really focus on, such as China."
Mr Archer said that although the UK cannot sign trade deals while it is an EU member, there will be numerous informal discussions taking place leading up to the Brexit date, which could be in late 2018 or early 2019.
According to Australian government trade figures, in 2014 Australia exported A$8.3bn (£4.5bn) to the UK in 2014 and imported A$12.4bn (£6.5bn).
But that is a fraction of the A$100bn (£55bn) exported that year by Australia to China, and the A$54bn it imported from the Asian giant.
And according to the latest data from the UK's HM Revenue and Customs for May 2016, Australia was 21st on the list of Britain's export markets, and 20th on the list of import providers.
BBC correspondent Phil Mercer, in Sydney
Britain is Australia's seventh largest trading partner, and is second only to the United States when it comes to direct foreign investment down under.
Australian Prime Minister Malcolm Turnbull said a free trade agreement with the UK was a priority, although such treaties are complicated and can be time-consuming.
Australia's recent trade deal with China, for example, took a decade to negotiate.
Mr Turnbull has said Canberra could also team up with New Zealand to strike new commercial and immigration accords with the UK following its decision to leave the EU.
Mr Fox, a prominent Brexit campaigner, said numerous non-EU countries had already asked Britain for a trade deal and he was "scoping about a dozen... to be ready for when we leave".
It comes amid reports he is preparing to fly to the United States next week for talks.
In April, President Barack Obama warned the UK it would go to the "back of the queue" for trade deals with the US if it voted to leave the EU.
Following the referendum, he said the UK's decision to leave raised "longer-term concerns about global growth".
Mr Fox told the Sunday Times: "We've already had a number of countries saying, 'We'd love to do a trade deal with the world's fifth biggest economy without having to deal with the other 27 members of the EU.'"