Rebel Tories claim they have enough support to inflict a humiliating defeat on Ms May, who is also under pressure from several cabinet ministers to stop counting overseas students as long-term migrants.
The issue will come to a head on Wednesday when MPs debate an amendment to the Higher Education and Research Bill passed by the House of Lords last month.
By 313 votes to 219, peers agreed that no student “should be treated for public policy purposes as a long-term migrant to the UK for the duration of their studies”.
Tory whips are trying to contain the revolt, pleading with the party’s MPs not to “rock the boat now” and urging them to defeat the Lords amendment.
But rebels claim they can overturn the Government’s majority of 17, which would require nine Tories to defy Ms May if all opposition party MPs join forces with them. They hope the real prospect of defeat will force the Prime Minister to compromise.
The backbench revolt leaves Ms May increasingly isolated on the issue. Downing Street has slapped down ministers who have called publicly for foreign students to be removed from the immigration statistics.
Amid claims that they feel unwelcome, the number dropped by 41,000 in the year to September. There are fears that, if the trend continues, universities would have to raise tuition fees above the £9,250-a-year ceiling taking effect this autumn.
Critics claim Ms May wants to drive down the number of overseas students to help her hit the Government’s target to reduce net migration below 100,000 a year.
Excluding the students would make that easier to achieve. Some 134,000 foreigners came to Britain to study in the 12 months to last September, during which net migration totalled 273,000.
The Independent and the campaigning group Open Britain, the successor to the Remain camp in the EU referendum, have launched a Drop the Target campaign urging the Government to abandon its aim.
Ben Howlett, Tory MP for Bath and a leading supporter of Open Britain, said: “International students should not be counted in the immigration statistics.
The Government has the chance to remove them when amendments to the Higher Education Bill come before the Commons next week. It is a chance ministers should seize with both hands.”
Rebels claim their ranks include MPs who voted Leave as well as those who backed Remain in the referendum, and several select committee chairs.
Neil Carmichael, Tory chair of the Education Select Committee, which took evidence from universities on the issue, said: “Higher education is an export industry for Britain which generates great value from international students, and no government should seek to make it harder for them to operate.
"The sector has serious concerns about any possible restrictions on the ability of international students to come to the UK. I look forward to a healthy debate when this amendment comes to the Commons.”
Anna Soubry, Conservative MP and a former business minister, said: “International students are of huge benefit to our universities and colleges and to our economy.
"When they have completed their studies and return home, their goodwill towards our country often results in business deals as well as improved international relations and understanding.
"The Government is showing welcome signs of pragmatism and common sense on immigration. I very much hope it will take international students out of the immigration figures.“
Even if the Government staves off defeat in the Commons, it would still have a battle on its hands. Peers say the Lords would refuse to back down when the bill returns to the second chamber.
There could then be a prolonged period of “ping pong” between the two Houses, delaying the Bill's passage beyond the current parliamentary session due to end next month.
The measure would encourage completion in higher education by making it easier for new providers to start up, award degrees and win university status.
Ministers pressing for a change on foreign students include Chancellor Philip Hammond, Foreign Secretary Boris Johnson, International Trade Secretary Liam Fox and universities minister Jo Johnson.
A Whitehall source said: “The ministers and many Tory MPs have made their position clear. Now it’s decision time for the PM.”
Ms May believes that including the students in the immigration figures increases the pressure on universities to stamp out bogus applications.
Allies say she wants to bring down net migration by reducing the number of overseas students, particularly at less prestigious universities, rather than changing the way the figures are compiled.
One said: “She thinks it would look like another fix and fiddle at a time when the public are cynical about politicians. She believes it’s important to regain trust.”
The Department for Education has said the Lords amendment would potentially prevent basic visa checks, or conditions being imposed on a student visa. The United Nations defines international students as long-term migrants.
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