Speaking at the G20 in China, Turnbull said both sides are keen to secure open markets.
“They've got to put in place free trade agreements and we are enthusiastic and supportive; we're providing Britain with as much assistance as we can at a technical level,” Turnbull said.
Before travelling to China, May was keen to put the UK's relationship with Australia in the spotlight.
Speaking ahead of the summit, Downing Street noted UK officials will this week hold talks with Australian counterparts about establishing a trade negotiating team, while the Australian government has also offered to dispatch negotiators to UK teams.
The UK government said New Zealand and Canada have also offered to share expertise.
“We are going to make a success of Brexit and one way we will do that is by playing to Britain’s strengths as a great trading nation and forging our own new trade deals around the world,” May said.
“We are building up the necessary expertise to go after these trade deals and, here in China, I will be seizing the opportunity to talk to leaders from countries like Australia, who have already made clear that they want to strike a deal once we have left the EU.”