A crackdown on foreign students doesn't go far enough and leaves the asylum system open to abuse, critics declared.
Labour on Tuesday claimed it has "stemmed" the "alarming growth" in protection claims from people arriving on legal routes.
The Home Office said a "significant increase" in visa application refusals led to a 10% fall in student asylum claims.
Officials attributed the drop to a "record number" of credibility interviews.
The think-tank, Migration Watch, said "it will not be sufficient to end the exploitation of this open backdoor route".
But Former Border Force Director General Tony Smith said: "Students should not be given a visa in the first place unless they can satisfy a visa officer that they have enough funds to pay for the course and support and accommodate themselves without working, and intend to return home after their studies."
Alp Mehmet, the Chairman of Migration Watch, said: "While I welcome this belated proposal by the Home Secretary, I would remind her that getting on for half the visas issued are to students, who are overwhelmingly heading to lower-ranking universities.
"Far from attracting the 'best and brightest', our student visas have become a wide open backdoor into Britain for those whose principal aim is settlement and the black economy.
"The Home Office must urgently introduce a cap, abandon the two-year post study work route, bring back interviewing before visas are issued and take back responsibility for who enters the country.
"International students cannot exist simply to keep low quality institutions afloat."
More than 5,000 Indian student visa holders claimed asylum in the year to June - despite India being the world's fifth largest economy and a democracy with free elections.
In total, more than 430,000 foreign students arrived in the UK in the year to June.
And the Home Office said the number of asylum applications from foreign students, workers or visitors soared to 41,400 in the year to June 2025.
This accounted for more than a third of asylum claims last year.

International students made up the highest proportion of claimants at 40%, followed by 29% from work visas and 24% visitors.
Stricter screening has seen refusal rates for short-term study visas increase from 45% to 68%, while skilled worker rejections surged from 3% in 2023 to 21% in June 2025.
A new Home Office communications campaign is also warning students they cannot overstay their visas.
Nearly 10,000 students and dependants received the guidance last week, with tens of thousands more expected to receive it over the coming weeks as their visa expiry dates approach.
The full message will read: "If you submit an asylum claim that lacks merit, it will be swiftly and robustly refused.
"Any request for asylum support will be assessed against destitution criteria. If you do not meet the criteria, you will not receive support.
"If you have no legal right to remain in the UK, you must leave.
"If you don't, we will remove you."
Cooper told BBC Breakfast that students are entering the asylum system and sometimes staying there for years, which "causes problems with asylum accommodation and hotels".
"We obviously will do our bit to support genuine refugees," she added, "but if nothing has changed in their country, people should not be claiming asylum at the end of a student course."
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