Theresa May has cast doubt on the feasibility of a points-based system for controlling immigration into the UK, one of the key promises of Leave campaigners during the EU referendum.
Speaking in China, the PM acknowledged people had voted for more control on the numbers of people moving to the UK.
But she questioned whether a points system, backed by Foreign Secretary Boris Johnson among others, would work.
She suggested it was not a “silver bullet” for addressing public concerns.
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Mrs May is attending the G20 summit of world leaders in Hangzhou, her first international summit as prime minister.
Having held talks with US President Obama and Russian President Vladimir Putin on Sunday, she will meet Chinese premier Xi Xinping on Monday among other engagements before heading home.
Mrs May has faced pressure to sketch out a vision of what Brexit will mean for the UK’s relations with key partners and major inward investors, such as the US and Japan.
In a briefing released to journalists on Sunday, the Japanese government expressed concern about the impact of the UK leaving the EU on its firms’ tariff-free access to the single market and their ability to recruit highly-skilled workers for its UK plants.
During the EU referendum, the Leave campaign said it backed an Australian-style points system for deciding the number of skilled and unskilled workers who could come into the UK every year from the EU and beyond – with numbers to be determined by MPs.
Recent figures showed that net migration into the UK remains above 320,000 – well in excess of the government’s stated target of reducing this to the tens of thousands.
By Laura Kuenssberg, BBC political editor
The now not so new prime minister has always promised to respect the referendum result, again and again vowing that Brexit means Brexit.
However, that might not entail the introduction of a points-based system to control immigration – the central proposal made by the victorious Vote Leave campaign during the referendum.
The prime minister vowed the government will deliver controls on the numbers of people coming to the UK from around the EU.
But Theresa May said one of the issues is whether or not points-based systems do work, suggesting that despite Vote Leave’s repeated promises, it might not be the answer.
This puts the prime minister not just at odds with several of her cabinet ministers who argued for such a system during the campaign. But potentially with some of the many millions of voters, in part persuaded to vote to leave because of that commitment.
As Theresa May has found at the G20 meeting, there are demands abroad as well as at home for more clarity on the government’s plans. But this is the first sign that one of the referendum’s winning side’s promises may not be kept.
Immigration points-based systems compared
Would a points-based system work for the UK?
Although Mrs May supported remaining in the EU, she has said that the Brexit vote must be respected and suggested that curbs on the current free movement of EU citizens into the UK would be a red line in future negotiations with the EU.
But she told journalists that exercising greater control did not necessarily mean a points-based system based on skills-based annual quotas.
‘Vote for control’
Asked whether she was concerned this was too blunt an instrument, she replied: “One of the issues is whether or not points-based systems do work. A lot of people talk about a points based system as always being the answer in immigration.
“There is no single silver bullet that is the answer in terms of dealing with immigration. You have to look across the board.
“You have to look at the whole range of issues, not just how you bring control through the rules you have for people coming in, but also making sure you are rooting out abuse in the system and dealing with people if they are discovered here illegally.”
She added: “People voted I think for control. What they wanted to see was control in the movement of people from EU countries into the UK.”
The government is expected to make a statement to Parliament this week on progress it has made on its Brexit strategy over the summer.
During a series of interviews, Mrs May declined to guarantee the UK would use money saved by leaving the EU to spend another £100m a week on the NHS or cut VAT on energy bills.