More than 50,000 English language tests taken by overseas students to extend their British visas have been declared invalid or questionable as a result of an official investigation into cheating on a huge scale.

Home Office ministers have suspended the overseas student sponsorship licences of one university – Glyndwr, near Wrexham – and 57 private further education colleges as a result of the investigation. Two further universities – West London and Bedfordshire – are no longer allowed to sponsor new students and, pending further investigations may also have their licences suspended.

Ministers have also ordered a fresh inquiry into wider migrant student abuses at all the London sub-campuses of universities based in other parts of Britain in the biggest investigation since the Home Office suspended the licence of the London Metropolitan University.

The Home Office immigration minister, James Brokenshire, announcing the measures in a statement to MPs, said a criminal investigation was under way into ETS Global Ltd, the European subsidiary of a US company, which is one of the biggest providers of English language tests in Britain.

He said the investigation followed allegations by the BBC1 programme Panorama earlier this year of systematic cheating at a number of the ETS test centres. "Facilitated by organised criminals, this typically involved invigilators supplying, even reading out, answers to whole exam rooms or gangs of imposters being allowed to step into the exam candidates' places to sit the test. Evidently this could only happen with considerable collusion by the test centres concerned."

Brokenshire said ETS had identified more than 29,000 invalid results and more than 19,000 questionable results at some of their test centres in 2012 and 2013. Brokenshire told MPs that as they have still to analyse results from a number of test centres the final figures will be higher.

The American firm, ETS, had its five-year contract to handle the national curriculum tests for schools in England and Wales terminated in 2008 after major delays in processing test results.

The National Crime Agency has been called in to assist the investigation, with some arrests already having been made. Immigration enforcement has also started to identify any overseas students who are in the country illegally as a result of a falsified test result. No evidence of systematic cheating has been found in the tests administered by the four other main providers of English language tests in Britain.

Since 2011 all overseas student visa applicants are required to prove they can speak English at an appropriate level. Brokenshire said was highly doubtful that many of the colleges or universities that were sponsoring them were fulfilling their duties as "highly trusted sponsors".

But he added that there were wider concerns about their conduct which justified a much deeper inquiry by the Quality Assurance Agency for Higher Education. He said that HMRC had uncovered evidence of overseas students earning more than £20,000 a year despite not being allowed to work more than 20 hours a week, and in one case a student been working a 60-hour week for six months.

He said that at Glyndwr University more than 350 students had been identified with invalid or questionable test results. At the second university whose licence is being suspended, West London, more than 290 had invalid or questionable results. Other universities with London sub-campuses have voluntarily stopped overseas recruitment while the investigation is under way.

Labour's immigration spokesman, David Hanson, welcomed the measures, saying the scale of abuse detailed in the statement was shocking. He demanded to know whether Home Office ministers knew about the scale of the abuse before the BBC investigation. "The system needs integrity. The minister needs to restore confidence today," he said.