Australia wants a free trade deal with Britain as soon as possible, new Prime Minister Theresa May revealed on Saturday.

In a phone call with her Australian counterpart, Malcolm Turnbull expressed his desire to open up trading with Britain promptly following the UK's decision to leave the EU.

Mrs May, who replaced David Cameron in Downing Street on Wednesday, described the call as "very encouraging" and evidence Britain can be successful outside of the EU.

Trade Secretary Liam Fox has been tasked with exploring such trading options, but Britain can not sign any deals while it remains an EU member.

According to Dr Fox, speaking to the Sunday Times, a number of non-EU countries have already asked Britain for a trade deal.

On Friday, Mrs May told Scottish First Minister Nicola Sturgeon she would not trigger Article 50 to leave the EU before getting UK-wide agreement.