Britain is pushing for a freedom of movement deal that will allow Australians to live and work in both countries without a visa.

The proposal was discussed by the UK's trade secretary, Liz Truss, and Australian Trade Minister Simon Birmingham in Canberra on Wednesday.

'It's certainly something we will be looking at as part of our free trade negotiations,' Secretary Truss said in a press conference at Parliament House.

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The proposal was discussed by the UK's trade secretary, Liz Truss, and Australian Trade Minister Simon Birmingham in Canberra (pictured)

Ms Truss said the UK would be 'looking at' the proposal as part of pre-Brexit trade talks with Australia.

'We want a fully comprehensive trade deal that reflects our deep, ongoing relationship, the friendship between our two countries, the fact that Australians want to come and live and work in Britain, and Brits want to come and live and work in Australia,' she said.

'The reason that I've chosen to make Australia one of the first countries I've visited as Trade Secretary is this is an absolute priority for me to get on with this trade deal.'

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

The proposal was rejected by Prime Minister Scott Morrison just last month after expressing he wasn't interested in a New Zealand-style agreement with the UK.

'The New Zealand arrangement is quite unique and it's not one we would probably ever contemplate extending,' Mr Morrison said following a meeting with British Prime Minister Boris Johnson.

Mr Birmingham said the trade deal could open up opportunities for Australia's agriculture sector.

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

Mr Johnson plans to take Britain out of the European Union on October 31.