The student loan system is at a "tipping point" as the government could be left with a multi-billion pound budget gap, according to scathing report from a group of MPs.

The Business, Innovation and Skills Select Committee called on the government to undertake an urgent review of the system.

The MPs expressed concerns that the Chancellor George Osborne's removal of the cap on student numbers may result in a multi-billion pound budget gap.

The group explained that the current student loan system for students residing in England, the government loses around 45p on every £1 ($1.71, €1.26) it loans out.

But the committee found that the Department of Business, Innovation and Skills (Bis) had a worrying record of miscalculating just how much it will lose on a student loan at the point it pays out.

The MPs said this "persistent error", resulting in the collection of £111m less than expected in 2011-12, had been compounded by the government's refusal to adopt a range of improvements suggested by independent forecasters.

"The government's estimates indicate the size of outstanding student debt will increase to more than £330bn by 2044," said Adrian Bailey MP, chair of the committee.

"With the prospect of a large potential black hole in the government's budget figures, government need to get its act together and properly calculate how much of these student debts are ever likely to be paid back.

"The government needs to set out a clear timescale for pushing ahead with a review of the overall student loans system because the alternative is an unfunded model which would leave students, universities, and taxpayers with a very raw deal indeed."

The MPs also argued that removing the student numbers cap is a worthy aspiration but raises concerns that the Chancellor's linking of this policy to sales of income-contingent student loans could result in an additional burden on the tax-payer.

Given the uncertainty around how much could be realised through these sales, the committee has called for the government to set out how the £5.5bn required between now and 2018-19 will be raised.

In addition, the committee recognised that sale of the income-contingent loan-book could bring a "significant windfall" to the public purse.

However, the MPs questioned the ability of Bis to get a good-return for the taxpayer.

The government's own commissioned analysis suggested that a current proposed sale would raise only £2bn rather than £12bn expected by government without an unusual (and potentially costly) deal made to protect the private investor.

"The problems of the new student finance system have largely been caused by the terms and conditions of repayment: graduates now pay back a much lower amount each month, and so take longer to repay their loans than under the previous system," said Dr Wendy Piatt, director general of the Russell Group.

"Graduates will now pay only 9% of their annual earnings above £21,000 – a far higher threshold than the £15,000 previously – and this is why projections for repayment are lower than under the old system.

"The government can, of course, change these repayment conditions in order to increase the amount of money repaid, if they so choose."

Bis had not responded to a request for comment at the time of publication.