May accused of backsliding on immigration after rejecting points-based system

"The people were clear in wanting a points-based immigration system which is why so many went out and voted to Leave the European Union. Any watering down from that will lead to real anger," insisted Mr Farage.

"Given that myself and others also campaigned for a migration system that would treat all who wanted to come equally, any preference for EU nationals would be totally unacceptable

"If the Establishment think they can stitch-up Brexit then they better be ready for the huge electoral consequences from a British public who on June 23rd voted for radical political change and now expect it to be delivered without failure," he added.

But Mrs May insisted that the Australian system would not succeed in giving Britain control back over its borders.

She told a press conference at the G20 summit in China: "What the British people voted for on June 23 was to bring some control into the movement of people from the European Union to the UK. A points-based system does not give you that control."

Mrs May said that as Home Secretary she was told by immigration officers that the most important thing the UK Government should focus on was students who had met the criteria to come to the UK but did not appear to be heading for a genuine course.

"Because they met the criteria, they were automatically allowed in; that's the problem with a points-based system,” declared the PM.

"I want a system where the Government is able to decide who comes into the country. That's what the British people want. A points-based system means that people come in automatically if they just meet the criteria."

Mrs May said there were "various ways" for the Conservative Government to assert control over migration into the UK but declined to elaborate, noting only: "We will be coming forward in due course with proposals."

She indicated that her drive to regain control over immigration would be balanced with the desire to get "the best deal possible" on trade for the UK in negotiations with other EU states.

"What we will be doing is working for the best deal for the United Kingdom.

"Yes, the voters' message on June 23 was clearly that they didn't want to see free movement continuing as it has done up to now. They wanted some control in movement of people from the EU into the United Kingdom.

"But we also want to get the best deal possible for trade in goods and services with the EU and I intend to go out there and be ambitious.

"There is a benefit not just for the UK of a good deal in trade in goods and services but a benefit for Europe as well," she added.

In London, her spokesman was asked if the Cabinet was as one on the issue of rejecting a points-based system and replied: “Discussions have gone on =and will continue to go on and we will be working flat-out to make sure we achieve the best possible result for Britain as we exit the European Union.”

Boris Johnson, the Foreign Secretary, regularly expressed support for a points-based system during the referendum campaign as did Liam Fox, the International Trade Secretary, Priti Patel, the International Development Secretary, Chris Grayling, the Transport Secretary, and Andrea Leadsom, the Environment Secretary.

Meantime, Japan's prime minister has urged Mrs May at the G20 summit to give more detail about her plans for Brexit amid concerns that his country's firms could be forced to pull investment from the UK.

Shinzo Abe said he wanted more "predictability" about the Brexit process and measures to ensure Japanese firms based in the UK would not suffer as a result of leaving the EU.

The two leaders met for brief talks in the margins of the summit in Hangzhou, following the publication of an extraordinary 15-page dossier listing Japan's concerns about the UK cutting ties with Brussels.

Mr Abe told the PM he attached "extreme importance" to the relationship with the UK and reminded her of the level of Japanese investment in Britain, which is partly due to membership of the EU single market.

"Prime Minister Abe requested her co-operation to enhance predictability and to continue to secure Japanese companies' businesses and value chains," Japan's ministry of foreign affairs said in a statement.

"In response, Prime Minister May mentioned that she recognises that the result of the UK referendum to leave the EU is having influence on the international community including Japan and expressed her hope that the Japan-UK economic relationships will be maintained and strengthened."

Japan's ambassador in London said he had spoken with executives at leading Japanese firms in the UK and none of them wanted to pull out. But he stressed that all options are open to the companies, which have a duty to their shareholders to remain profitable.

Koji Tsuruoka told the BBC hundreds of Japanese companies had operations in the UK, adding: "They are companies responsible to their stakeholders and their duty is to produce profit.

"If the way Brexit ends up does not provide companies with a prospect of making sufficient profit to continue operating in the UK, of course there is no option that they can't choose. All options are open to them."

Asked whether that could mean a company like Nissan closing its car plant in Sunderland, Mr Tsuruoka replied: "These are exactly the predictions that are going to hurt the future of the economy because these decisions have not been made.

"I have been talking to a number of Japanese business leaders operating in the UK and they all agree that the UK is the best place to do business in Europe. They want to continue to operate from the UK, and the list of issues we have put out to the UK as well as the EU are issues that they are seeking to achieve.

"However, there is a negotiation that will have to be conducted and if these requests are not met, then it will be for industry to decide what to do.”

The ambassador said it was very difficult to imagine that all Japanese companies - including the auto companies - would pull out in totality from UK because its UK economy was vibrant and it would be a good market for manufacturers to continue to sell their cars.

"The problem we will have to confront is: what is the market that could be accessed for production outside of the UK? If there are conditions that block Japanese auto makers' cars being exported to continental Europe, such as customs duties, that, of course, will affect the competitive nature of the pricing of the cars.

"But that is also something that can be affected by the currency exchange rates as well. It is not just customs duties."

Mr Tsuruoka said Tokyo wanted to see a "well thought-through consideration" of the issues before formal talks on the UK's withdrawal from the EU begin, and welcomed Mrs May's "cautious and very patient" approach to the invocation of Article 50.

Japan accepted that Brexit would happen, as a democratic decision of the British people, he said. But the ambassador warned that European and international economies could be damaged if withdrawal harms the UK economy, adding: "Therefore we have a very important stake in making Brexit a success that will not damage or hurt the global economy."

Mrs May insisted countries including Japan were "confident" about the UK's future.

Asked about her meeting with Mr Abe, she said: "We were both very clear that we will be working together to ensure that we can maintain and build on our relationship.

"And if you think about it, the single biggest vote of confidence in the UK in terms of inward investment, since the referendum, was from a Japanese company - from Softbank and its £24 billion proposal to buy ARM."

Challenged to guarantee that jobs at Japanese car factories in the UK were safe, the PM said: "What I have found good about the discussions I have had with a number of world leaders, including the discussions I have had with prime minister Abe, is the willingness from other countries to talk to the UK about future trade arrangements and the confidence that they have in the UK."

She added: "I am confident and others have been confident about the relationship we can build with them."