The breakneck expansion of private colleges should be investigated by the government spending watchdog, the chair of the powerful public accounts committee said yesterday.

Margaret Hodge MP, a former Labour education minister, said she had asked the National Audit Office (NAO) to draw up a report following what she said were shocking and serious allegations about the potential misuse of millions of pounds of public money.

She said there had been an astonishing growth in private colleges, which had benefited from increased access to public funds – from £40m in 2010 to £900m this year – after the higher education minister David Willetts brought in reforms allowing the sector to use student loan financing .

Hodge's intervention comes after a Guardian investigation revealed that one college that had tripled in size since the rules were relaxed in 2012 was running poorly attended classes with tiny numbers of students.

A four-month Guardian investigation revealed on Wednesday that senior staff at the London School of Science and Technology (LSST), a college in Wembley, north-west London, alleged the institution was running classes with low attendance . The institution was referred to locally as "the cashpoint" because it offered quick and easy access to student finance.

When the Guardian filmed undercover at the college it found a classroom that had a lecturer but not one student.

The organisation of the school demonstrates flaws in the planned expansion of privately run higher education colleges unveiled by Willetts in 2011. Little known institutions were allowed to recruit students without a cap on numbers or on the cost to the taxpayer.

Speaking in her office at the House of Commons, Hodge said she was taken aback by the footage of students talking about how they could sign up for the loans and then not bother to attend classes.

"I'm pretty shocked," she said. "[The Guardian] has raised some huge issues. We're talking about many hundreds of millions, if not a couple of billions in taxpayer money that was set aside to support higher education."

Hodge said it was potentially a misuse of public funds and that money may have been taken "out of the system to enrich individuals and colleges".

She said she felt sympathy with genuine students who expected better for their £5,000-£6,000 in tuition fee payments and may not have been receiving the best education.

Willetts has previously said that opening higher education to little-known private colleges would raise standards and create innovation throughout the sector.

However, Hodge said there was a pattern emerging in which the government opened sectors to private institutions and only then set up proper regulatory frameworks to check public spending and "follow the taxpayer's pound".

"You've just got to look at the [growth] figures," she added. "The red light ought to go on immediately."

Hodge, known for her formidable questioning of civil servants and company executives, said she felt culpable for not acting more on warnings about the potential for the misuse of public money from Sally Hunt, general secretary of the University and College Union, which represents lecturers, when she wrote to the committee in 2013. "We didn't take her allegations seriously enough at the time."

Hodge said she also regretted not holding Willetts's Department of Business, Innovation and Skills to greater scrutiny. "At that time we should have said: 'Have you got the systems in place to monitor whether or not the money is going to the purpose intended?'"

She said that, after the NAO report, she would hold Business Department civil servants to account for the allegations.

"They are accounting officers in government, and they will have to be brought in front of us to account for why they allowed this loose system to exist; why they didn't see any of the warning lights."

London School of Science and Technology, where the Guardian filmed undercover. Photograph: Graeme Robertson for the Guardian

Hodge added: "I will ask the comptroller auditor general to prepare a report for my committee on the basis of which I will take evidence. It will take us a few months, but I think you have brought to our attention a huge issue … it may be one I've seen in other guises … there's an outrageous waste … misuse of public money."

LSST denied the allegations put to them and said the Guardian had visited the college at the end of term when students were submitting their coursework. The college said it had "robust procedures for recording and monitoring student attendance" and employed a full-time attendance officer.

However, Willetts, who has compared the reforms to the education secretary Michael Gove's free schools, said that while action to toughen up controls on private colleges was under way, the emerging private-college sector remained significant.

"These colleges have an important role to play in providing students with an alternative to university. But students and the taxpayers who provide funding deserve to get a quality service," he said.

Hunt showed the Guardian letters her union had written to Willetts specifically warning of the dangers associated with his plan to allow unproven, for-profit colleges to recruit without limit. In reply Willetts insisted the robust quality assurance regime in England would prevent malpractice. He also said publicly that his doubters would be proven wrong by the innovations that private providers would foster.

In response to Hodge's call for NAO involvement, Hunt said: "We raised the issues of for-profit colleges' access to public money and our concerns about standards time and again with ministers.

"We were ignored at every turn by a government that seemed so blinded by the ideology of competition that it refused to heed our warnings.

"We are delighted the Public Accounts Committee and the National Audit Office are now looking into the matter. We have heard nothing from ministers or the colleges to explain why this situation was allowed to happen. We trust they will not be able to shy away from a Parliamentary watchdog."

A Business Department spokesperson said they would co-operate fully with any NAO investigation.