Australia will push for more business, student and work visas for its citizens in the UK, as part of a new trade deal after Brexit.

On Friday, Foreign Minister Julie Bishop said this was "obviously" something that could be part of the free trade agreement that the countries have agreed to negotiate after the UK leaves the European Union.

"Being able to live, work or spend time, study in each other's countries is something to which we would aspire," she said.

"Should we be in the position to conclude a free trade agreement after Brexit then obviously this can be the subject of a free trade agreement. It's something that we were able to achieve with the United States.