THERESA May has rubbished adopting a new points based system to control immigration when Britain leaves the EU – casting deep doubt on if it would cut numbers.

The PM’s attack on the Australian-style system is a slap down for Foreign Secretary Boris Johnson and the Vote Leave campaign, who championed it as their flagship EU referendum policy.

5 Theresa May questions whether points-based immigration system work and seems to be suggesting a visa system would work better Credit: Alamy

5 The Prime Minister spoke about the issue of immigration while at the G20 summit and her words are likely to disappoint some Cabinet ministers Credit: Reuters

It also threatens to open up a major new Cabinet Brexit rift.

Five current ministers around Mrs May’s top table are on the record as calling for a points based system - Boris, Liam Fox, Andrea Leadsom, Chris Grayling and Priti Patel.

But expert immigration campaigners have long dismissed it as wrong for the UK.

Speaking at the G20 summit in China, Mrs May argued: “People talk about a points based system as always being the answer on immigration.

“One of the issues is whether points based systems do work."

5 Foreign Secretary Boris Johnson will be disappointed to learn Theresa May does not support his idea of a points-based immigration system Credit: EPA

Insisting it wasn't necessarily what Brexit backers voted for, the PM added: "The voice of the British people is very clear, they wanted control over movement of people coming in from the European Union. "We will be going out to deliver on that.”

Revealing her frustration with Vote Leave’s calls, Mrs May added: “You really don’t want to ask a former Home Secretary about the intricacies of points based systems because it might take a very long time answering your question, I have to tell you.”

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Instead, the PM said: “There is no single bullet that is the answer in terms of dealing with immigration.

“You have to look across the board - not just how you bring control for the rules you have for people coming in, but also making sure you’re rooting out abuse in the system, and dealing with people here if they’re discovered illegally.”

Mrs May’s intervention as ministers look to draw up a new immigration system for Brexit suggest she wants a system based on visas for all new arrivals instead.

5 Theresa May has addressed the issue of immigration while in China for her first G20 summit since becoming Prime Minister Credit: Getty Images

5 Brexiteer Priti Patel is on the record as being one of the five government ministers who want an Australian-style immigration system Credit: Getty Images

The new PM also last night cast doubt on whether two other Vote Leave pledges would come true when Brexit happens.

She refused to commit to slashing VAT from fuel bills or spending £100m a week more on the NHS from former EU budget contributions.

Leading immigration pressure group Migration Watch branded a points based system for non-EU immigrants “a disastrous failure” when the last Labour government tried to set one up.

Its chairman Lord Green argued that Australia’s net migration is three times higher than the UK’s as a proportion of their population.

Brexit deal could see Britain paying Brussels millions BRITAIN could still end up paying millions to Brussels for years as part of a Brexit deal, Theresa May has signalled. Some EU leaders have insisted the UK would have to continue making financial contributions into the EU budget in exchange for access to the single market.

Quizzed directly by The Sun, the new PM refused to rule out the cash payments as making up a part of her Brexit negotiation.

Mrs May insisted: “What we need to be doing is making sure we can get the best possible deal for the United Kingdom when we leave the European Union.

“But I’m not going to give away my negotiating hand.”

Bringing home all £350m a week that Britain is currently on the hook for TO Brussels was a major promise of the Vote Leave campaign.

Mrs May also refused to rule out pushing for Britain to retain full membership of the single market when we leave, despite EU bosses insisting that meant accepting full freedom of movement – which she last week ruled out.

Instead the PM said: “I don’t take anything for granted. I want to be ambitious”.