The ban – which affects all overseas students except those on postgraduate courses and certain scholarships – will slash migration by tens of thousands, Mr Cleverly claimed.
The move was announced in May by his now sacked predecessor Suella Braverman, just as official figures showed net migration running at 672,000.
Later figures showed it had hit a record high of 745,000, sparking outrage from right-wing Tory MPs, who demanded fresh action from Rishi Sunak’s government.
Experts have warned that the restrictions on dependents joining overseas students in the UK could affect universities, which rely on the income generated via the fees paid by foreign students, and could harm the UK’s reputation as an international destination.
As of Monday, international students starting courses in Britain will no longer be allowed to obtain visas for their spouses and relatives unless they are on a postgraduate research programme or a government-sponsored course.
Mr Cleverly said the government had a “tough plan to rapidly bring numbers down”, and that he was “ending the unreasonable practice of overseas students bringing their family members to the UK”.
The home secretary added: “This will see migration falling rapidly by the tens of thousands and contribute to our overall strategy to prevent 300,000 people from coming to the UK.”
Immigration minister Tom Pursglove said universities had seen “a surge in the number of dependants being brought by students, which is contributing to unsustainable levels of migration”.
In November, Tory MPs on the right demanded fresh action by Mr Sunak to cut immigration, as revised figures from the Office for National Statistics put annual net migration at a record figure of 745,000.
Responding early in December, Mr Cleverly set out a raft of new restrictions that he said would cut numbers – including hiking the salary threshold for Britons bringing foreign spouses to the UK to £38,700.
The move was criticised for threatening to tear families apart, with many fearing that their future plans had been thrown into doubt as the government considered the details of the policy.
Ministers later U-turned, though only in part, by quietly announcing that the threshold would first be raised to £29,000 and then increased in “incremental stages” until the spring of 2025. This sparked fresh anger from right-wing Tory rebels, who want to see much tighter migration controls.
The Home Office said the visa package that comes into force on Monday represents a “tough but fair” approach – insisting that the changes to student visas will still allow colleges and universities to attract “the brightest and best”.
But the government said it was “removing the ability for institutions to undermine the UK’s reputation by selling immigration, not education”.
Experts have previously expressed concern about the 1 January visa changes. Nick Hillman, director of think tank the Higher Education Policy Institute (Hepi), warned that international students could instead travel to competitor nations to undertake their studies.
“As a country, we risk cutting off our nose to spite our face,” he warned. “International students benefit the UK ... they are vital to maintaining our world-class university sector as their fees cross-subsidise the teaching of home students and also help to fund UK research.”
Labour has backed the restrictions for overseas students who are enrolled on shorter courses – but said they do not go far enough to tackle “deep failures” in skills and training across the UK labour market, or to boost the country’s sluggish economy.
“This is nothing more than a sticking plaster,” shadow home secretary Yvette Cooper said. “The Tories’ complete failure to tackle skills and labour market problems is undermining growth as well as increasing migration.”
Mr Cleverly has faced calls to resign over Christmas after joking about spiking his wife’s drink with a date-rape drug at a reception in Downing Street. The home secretary apologised, and No 10 said Mr Sunak considered the matter closed.
Mr Sunak boasted in his new year message that he had taken “decisive action” to stop illegal migrant boats in the English Channel.
However, he is facing calls from rebel MPs in his own party to toughen up his Rwanda Bill and get deportation flights started by the spring. MPs on the right have threatened to kill the bill if the government does not agree to amendments in the new year.
And top legal adviser David Pannick is said have warned Mr Sunak’s government that the Rwanda Bill may not enable deportation flights to begin because it still allows for individual legal appeals to be submitted.
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