An earlier version of this story appeared on PoliticsHome.
Under the scheme, foreigners wishing to come to the UK would need to have enough points, based on their skills and experience, before being allowed in.
On her way to the G20 in China, UK Prime Minister Theresa May said there was no "silver bullet" to reducing numbers and cast doubt on the effectiveness of a points-based system (PBS).
But her official spokesperson went even further this morning by ruling it out completely.
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She said: "One of the opportunities of Brexit is that we will be able to control the number of people coming to Britain from the EU.
"The precise way in which the government will control the movement of EU nationals to Britain after Brexit is yet to be determined.
"However, as the Prime Minister has said many times in the past, a PBS will not work and is not an option."
The spokesperson added: "When Labour introduced a PBS, the numbers went straight up.
"In Australia, they have a PBS, and they have higher immigration per capita than Britain.
"A PBS would give foreign nationals the right to come to Britain if they meet certain criteria: an immigration system that works for Britain would ensure that the right to decide who comes to the country resides with the government."
Speaking to reporters yesterday, May also rejected suggestions that those who voted for Brexit did so because they wanted a points-based system.
"People voted, I think, for control," she said. "What they wanted to see was control of the freedom of movement of the European Union countries into the United Kingdom."
And May stopped short of saying she wanted to see the end of freedom of movement - leaving open the possibility that citizens of some EU countries will still be able to come to Britain unhindered.
She said: "I think what people wanted to see, what came out of the vote, is control. They wanted to see an ability to be able to control the movement of people from the European Union.
"And obviously that's what I say, not free movement as it has been in the past. And we need to respond to the voice of the British people."
The UK has faced backlash over its plans to limit the number of EU migrants coming into Britain, with many EU policymakers warning that the country would not be allowed to access the single market without also allowing freedom of movement.
Most recently, European euro and social dialogue Commissioner Valdis Dombrovkis warned that the UK cannot "cherry pick", and that access to the single market would come with respect for other Union rules and regulations - including free movement.
Outgoing Ukip leader Nigel Farage, who co-chairs the European Parliament's EFDD group, was highly critical of May's comments.
"There is already huge anxiety out there in the country regarding Theresa May's reluctance to trigger article 50," he said.
"Her rejection of the type of migration system so many went out there and voted Leave to see implemented indicates serious backsliding.
"Those of us on the Leave side were perfectly clear in campaigning for strong border controls outside of the EU.
"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," he warned.