LONDON (Reuters) - Australian Prime Minister Malcolm Turnbull told his British counterpart Theresa May he would like to see the two countries strike a free trade deal as soon as possible following Britain's vote to leave the EU, May's office said on Sunday.

The two leaders had spoken on Saturday to discuss their priorities after May took office on Wednesday and Turnbull retained power a week ago in a national election.

Turnbull had congratulated May, her office said in a statement, and "expressed a desire to strike a free trade deal as soon as possible".

While acknowledging that legal obligations prevent Britain from signing deals while still an EU member, May had replied she would be very keen to complete an agreement as soon as possible, the statement added.

"I have been very clear that this government will make a success of our exit from the European Union," it quoted her as saying afterwards. "One of the ways we will do this is by embracing the opportunities to strike free trade deals with our partners across the globe."

She added: "It is very encouraging that one of our closest international partners is already seeking to establish just such a deal."

Britain's June 23 vote to leave the European Union means the world's fifth largest economy will have to negotiate new trade deals with Europe and other major markets in talks that could take years.

The European Commission hammers out trade deals on behalf of EU countries, meaning Britain has not negotiated its own deal since it joined the bloc in 1973.

May has said she will not start the two-year process for Britain's exit from the EU this year and it is not clear when Britain could start new trade talks.

(Reporting by Kate Holton and Stephen Addison; Editing by Kevin Liffey)