There are concerns that "rogue agents" are targeting private schools to traffic young Vietnamese students to the UK, according to reports.
Robin Fletcher, chief executive of the Boarding Schools' Association, said that in the past two to three years, boarding schools had been made aware of a "small number" of concerning cases regarding students from Vietnam.
The association issued a warning to its members advising "extreme caution" when accepting students from Vietnam. The Independent Schools Council issued a similar warning in 2017.
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It followed cases where Vietnamese students went missing within weeks or months of arriving at British schools, an issue highlighted inThe Times.
The students, who are under 17 years of age, arrive in Britain on Tier 4 child visas, which are sponsored by independent schools.
"A small number of criminals and rogue agents have tried to exploit the system and use some schools to traffic children," Mr Fletcher said.
"On the very rare occasion this has happened, our schools followed proper procedures, reporting to the Home Office and police, and worked with all agencies to track down and secure the welfare of the pupils involved.
"We have advised all our members to be vigilant when recruiting any students from Vietnam and have also worked with schools to inform the Home Office about any issues."
Brooke House College principal Mike Oliver said two students "absconded" from his school in Market Harborough, Leicestershire, in the 2015-16 academic year.
Mr Oliver said relevant authorities were notified and the students were found by police.
"A further subsequent Home Office inspection confirmed that the college was fully compliant with all visa requirements as stipulated by them as a Tier 4 sponsor," he said.
Independent Schools Council chief executive Julie Robinson said the council works with the Home Office to ensure the visa system is not exploited by criminals.
"A small number of criminals have sought to exploit the immigration system and the ISC has issued guidance to members advising extreme caution and vigilance when recruiting from Vietnam," Ms Robinson said.
The news comes less than two weeks after 39 migrants, believed to be Vietnamese, were found dead in a lorry in Grays, Essex.
The discovery put a spotlight on international people-trafficking gangs, with reports that Vietnamese families were paying thousands of dollars to gangs to help loved ones travel abroad.
The Home Office said 702 potential Vietnamese victims of modern slavery were referred to the National Referral Mechanism in 2018.
It added that schools with Tier 4 sponsor licences were checked to ensure they fully complied with UK legislation and regulation.
"Educational establishments have a duty to report a lack of enrolment or disappearance to us. When the location of a child is unknown, this is referred to social services and the police," a spokesperson said.
Approximately 666 independent schools have Home Office approval to sponsor overseas students for child visas.