May was already issuing cautious noises on the plan overnight, telling reporters at the G20 that a points system, would not be a "single silver bullet".
And now Downing Street has moved to entirely ruled out a new system based around awarding points for categories of migrants based on various criteria, including working history.
A spokesman for May said today: “It is clear that a points-based system doesn't work and is not an option going forward.”
May is understood to have rejected the options, in part, after noting a similar system in Australia has left the country with a higher net migration ratio than Britain does now.
May met with Australian Prime Minister Malcolm Turnbull at the G20 earlier this week, although it is not known whether she discussed the system with her counterpart.
However, new controls on migration such as an annual cap remain under consideration, although Downing Street declined to comment on exactly which measures the Prime Minister would explore.
It comes despite June's referendum vote, which saw the official Leave campaign, fronted by now foreign secretary Boris Johnson, propose “an Australian style points-based system”.
Johnson and international development secretary Priti Patel are among the ministers to have pushed for the points option in particular as part of the Vote Leave campaign.
Indeed, May's comments actually mimic that of the Remain campaign - in one televised Brexit debate, then energy secretary Amber Rudd rubbished Johnson's proposal of a points system, saying that there was "no silver bullet".