SYDNEY - Britain's Trade Minister Liz Truss said on Wednesday she expects to complete a wide-ranging trade deal with Australia within months of exiting the European Union.

In efforts to reduce the economic impact of Brexit, Britain is looking to line-up a series of trade deals with smaller, non-EU countries.

Truss - who is in the middle of a three-nation tour that includes Australia, New Zealand and Japan - said she expects a quick conclusion to trade talks that will begin when Britain leaves the EU.

"The reason that I have chosen to make Australia one of the first countries I have visited as trade secretary is because it is an absolute priority to get on with this trade deal," Truss told reporters in Canberra.

"I would say months rather than years for it to be completed."

British Prime Minister Boris Johnson has said he will take the country out of the EU on Oct. 31 with or without a deal with Brussels.

But the British parliament this month passed a law that requires Johnson to ask the EU for a three-month delay to Brexit if a deal is not approved by Oct. 19.

Two-way trade between Australia and Britain is worth A$26.6 billion ($18.22 billion), Australian data shows.

Britain is Australia's seventh-largest trading partner, the data shows.

Australia's Minister for Trade Simon Birmingham said a trade deal with Britain will particularly benefit the country's agricultural sector, worth around A$60 billion.

"As part of the EU, market access to Britain in terms of agricultural products has been limited," Birmingham told reporters. "This is something we will look to address."

($1 = 1.4596 Australian dollars)

(Reporting by Colin Packham; Editing by Jacqueline Wong) ((colin.packham@thomsonreuters.com; +61-2 9321 8161; Reuters Messaging: colin.packham.thomsonreuters.com@reuters.net))