A government watchdog has launched an investigation into the Home Office’s decision to accuse about 34,000 international students of cheating in English language tests, and will scrutinise the thinking behind the subsequent cancellation or curtailment of their visas.

More than 1,000 students have been removed from the UK as a result of the accusation and hundreds have spent time in detention, but large numbers of students say they were wrongly accused. Over 300 cases are pending in the court of appeal as hundreds attempt to clear their names. MPs have warned that this immigration scandal could be “bigger than Windrush”.

The National Audit Office (NAO) has been making preliminary inquiries into the government’s handling of the issue since the beginning of the year, and has now announced that it will proceed with a formal investigation. The body is expected to report its findings in late May or June.

“In 2014, a BBC Panorama documentary drew attention to fraud in the UK student visa system, including widespread cheating in English language tests. The Home Office revoked student visas where there was evidence of cheating, but its decisions have come under renewed public and parliamentary scrutiny in the wake of the Windrush scandal,” the NAO said. “The NAO is looking at the information held by the Home Office on the number of people alleged to have cheated and the action the Home Office has taken to date.”

Undercover filming by the BBC in 2014 showed clear evidence of cheating in two test centres where international students sat the test of English for international communication (Toeic). Reporters showed the footage to Theresa May, then home secretary, who said she was shocked, and promised to take action. The Home Office concluded that around 34,000 of the 58,458 students who had taken the test between 2011 and 2014 had definitely cheated, that a further 22,600 had “questionable results”, and that only 2,000 had definitely not cheated.

Campaigners have questioned whether it is plausible that such a large proportion of students sitting a Home Office-approved test could have been involved in cheating.

Stephen Timms, the Labour MP for East Ham, who represents a number of affected students and who has been campaigning on this issue, said: “I welcome the NAO’s decision to investigate the Toeic scandal on behalf of parliament. I hope we might finally find out why so many innocent students have been treated so disgracefully.”

Nazek Ramadan, director of Migrant Voice, a charity that has been assisting those affected for several years, said: “This is an important step on the road to justice for thousands of innocent students. Many were wrongly accused and have spent the last five years trying to clear their names in the courts. Most remain trapped in a legal labyrinth, facing Home Office appeals and delays at every step and living with the daily threat of detention and deportation.

“Stripped of the right to work, study or even access healthcare, many of the students are destitute and suffering from severe mental health problems. The criminal allegation against them means that they cannot continue their studies, get a good job or obtain a visa to travel anywhere in the world. The Home Office’s handling of this issue has been spectacularly unfair and opaque, and it’s high time the truth was brought to light.”

A Home Office spokesperson said: “We have been supporting the National Audit Office in its work on this investigation since the start of the year. We will consider the findings of the report once it is published.”

Last year the NAO published a critical report on the Home Office’s handling of the Windrush scandal, highlighting poor-quality data that wrongly classified people as illegal immigrants, the risky use of deportation targets, poor value for money offered by hostile environment policies, and a failure to respond to numerous warnings that the policies would hurt people living in the UK legally.