London: A trade deal between Australia and the UK could be struck within weeks after Brexit, Trade Minister Simon Birmingham has said, after talking to his new British counterpart Liz Truss.

That could be as early as November this year, amid growing signs new Prime Minister Boris Johnson is pursuing a No Deal Brexit on October 31.

Liz Truss phoned her Australian counterpart for their first official discussion. Credit:Bloomberg

Truss, a free-market Libertarian, was one of the big winners of Boris Johnson's cabinet reshuffle, being promoted from the junior ministry to the Cabinet, replacing Liam Fox as Trade Secretary.

Truss had wanted to be made Chancellor of the Exchequer but that job went to Sajid Javid, one of the leadership contenders who backed Boris Johnson after being knocked out.