Britain's most senior taxman has admitted making "governance errors" when agreeing multibillion-pound settlements with large companies.

Dave Hartnett, HMRC's head of tax, has conceded that Revenue officials did not follow correct procedures in two high-profile cases that could have left taxpayers millions of pounds out of pocket.

The errors are understood to relate to claims that Vodafone faced a £6bn tax bill – a figure HMRC has described as "urban myth" – but paid only £1.25bn to settle the dispute. There are also suggestions US investment bank Goldman Sachs avoided £10.8m of tax payments last year.

Hartnett told a Treasury select committee that HMRC settled a tax dispute without informing all members of its oversight board. "There was one where a settlement without the whole of the high risk corporate programme board being consulted before the taxpayer was told the case was settled," he said.

In the other case an official neglected for a time to inform the board, leading to a delay which could have resulted in less tax being collected.

The high risk corporate board's supervision is meant to ensure tax officials do not agree settlements in private deals.

"We have a process laid down, and it was not fully followed," Hartnett said, according to a transcript of the hearing published on Tuesday. "The process is designed to ensure that for cases over a particular amount of money, there is broad oversight among our tax leaders of a proposed settlement."

Hartnett refused to explain exactly what went wrong, how much tax may have been lost or confirm which companies may have escaped their full tax commitments.

Jesse Norman, a Conservative member of the committee, said parliament was being prevented from discovering whether or not taxpayers have been left out of pocket.

"There is significant public concern that recent settlements with Vodafone and Goldman Sachs have not been properly handled and have resulted in smaller payments than were in fact due.

"Yet Mr Hartnett has refused even to indicate whether interest was paid by Vodafone on the tax due, despite confirming that it is an offence not to pay interest on tax owing."

Norman said the tax system is "disfigured by a lack of accountability", and called for greater parliamentary and ministerial oversight.

"At present MPs can be briefed in confidence by the intelligence services, yet cannot find out any details of improper private tax deals done by the taxman. Even Treasury ministers are left in the dark."

Norman said evidence of HMRC's "governance errors" came to light only after a National Audit Office investigation.

Vodafone's settlement, which led to widespread protests, saw HMRC collect £1.25bn to draw a line under a long-running investigation into its 2000 takeover of German rival Mannesmann. Leaks from the department suggested HMRC had wanted to collect up to £6bn from Vodafone.

Chuka Umunna, the shadow minister for small business, has said Goldman avoided £10.8m in tax when the case was dropped last year. Private Eye claims to have seen internal documents that show Hartnett failed to follow standard guidelines applied to other tax disputes when he settled the dispute with Goldman.