Study is the most common reason for people coming to the UK for more than a year and seven in 10 people would like to see a cap imposed, the poll of almost 3000 adults showed.
Britons also backed tough action over immigration offences, with most saying bogus students with insufficient English skills, those working instead of studying, and those who have overstayed their visas should all be deported.
The survey of 2910 Britons for the campaign group Migration Watch UK found 70% said there should be a limit on the number of foreign students coming to Britain, while only one-fifth (22%) were opposed.
Those polled were told that some 250,000 foreign students from outside the EU come to the UK every year to study, providing universities and colleges with valuable income, and about one in five stay on legally. But the lack of exit checks means it is not known how many go home at the end of their studies.
A different poll of more than 1000 people last year by the Migration Observatory at the University of Oxford found only one in three people wanted student immigration reduced.