The comments by Mrs Rudd, a prominent campaigner for Britain staying in the EU betray a split within the Tory cabinet over the idea, with the Foreign Secretary Boris Johnson promising to campaign for change just last month at a joint media conference with Foreign Minister Julie Bishop.

Mrs Rudd also poured cold water on the idea of a free movement zone for Brits and Australians, as is being pushed by former Prime Minister Tony Abbott who is in London and due to appear at a fringe event hosted by the conservative Spectator magazine on Tuesday local-time.

Prominent Leave campaigners including the conservative Member of European Parliament Daniel Hannan, raised the prospect during the EU Referendum campaign, in which the estimated 87,000 Australians living in Britain were entitled to vote.

When asked by Fairfax Media if there was any chance free movement or relaxed visa requirements might become reality post-Brexit, Mrs Rudd ruled out the idea.

"There are no plans to increase immigration from Australia," Mrs Rudd said.

The Home Secretary praised an existing visa young person's access scheme as "particularly very good."

Mrs Rudd said everything is under review but cautioned: "I do think that particular scheme does work very well so I wouldn't envisage any change," she said.

Mrs Rudd was a prominent campaigner for the Remain campaign but was appointed Home Secretary by Prime Minister Theresa May. Mrs May has been criticised for having not released details about how Britain's exit from the EU will take shape, apart from her now commonly mocked refrain "Brexit means Brexit."

Asked how difficult it was to sit in a Cabinet dominated by Leavers, shed told an audience at a fringe festival hosted by The Times she accepted the result.

"We know some things about what Brexit means but there's a lot within that that we don't know, 'Brexit means Brexit' but there's a lot to be negotiated and discussed," she said.

The Home Secretary's comments are a blow for Australia which is urging the British government to relax its tough rules for lower-paid migrants but also in stark contrast to the Foreign Secretary Boris Johnson, a noted Australiaphile's recent commitment to campaign for change.

"To my mind, I think it will be a fantastic thing if we had a more sensible system … this is something where I think we can make progress and I am confident that we will," Mr Johnson said during a joint-media conference with Foreign Minister Julie Bishop in London last month.

Australia believes its best chances of securing Australians an easier chance to work and live in the UK lie in any future trade deal which both countries are keen to strike once Britain leaves the EU.

"It is something that we were able to achieve with the United States and I certainly look forward to an increasing number of business visas, student visas and work visas between Australia and the UK. We have significant equities here. Australia is a significant investor in London in particular," Ms Bishop said at the same media conference.

In a bid to curb its migrant intake, the British government began deporting those who earn below £35,000 ($70,000) per year.  But because of its membership of the single market, it is obliged to allow in workers from EU member countries like Bulgaria and Romania, regardless of their skills.

Net migration to the UK in 2016 is 300,000 and well over the government's target of 100,000. Net migration from EU countries is 184,000, which is just short of the total for the 188,00 migrants from non-EU countries combined. Britain will be able to drastically cuts its migrant intake from EU countries once it formally leaves the union.

Mrs Rudd wants to reduce the net migration to the "tens of thousands" by 2020 when the next general election is due.

James Skinner from the Canadian-based Commonwealth Freedom of Movement Organisation said he placed more stock in the commitments made by the Foreign Ministers.

"If Mrs Rudd has no plans to promote free movement or relax visas at this time, she certainly will in the near future," Mr Skinner said.

"Over 164,000 people have signed our online petition for free movement between the UK, Australia, New Zealand and Canada, and only recently, Boris Johnson and Julie Bishop discussed the tremendous potential for visa liberalisation between the UK and Australia. "

"Mrs Rudd's comments are certainly unrepresentative of the general population."

Prime Minister Theresa May will formally trigger Article 50, the formal process for leaving the EU in March 2017. Britain will have two-years to negotiate its exit but Cabinet Ministers have suggested it could occur sooner than 2019.

Fairfax Media