A government minister who criticised Labour mayoral candidate Ken Livingstone for avoiding tax is an investor in a firm that also uses tax breaks, and has failed to declare it to parliament.

Stephen Hammond, the transport minister, is a partner in Harwood Film Partnership, which has deferred tax for its partners. His involvement has not been declared in the parliamentary register of members' interests.

Hammond's partnership may well come as an embarrassment to the Tories. This spring George Osborne described those involved in aggressive tax avoidance as "morally repugnant".

Hammond was at the forefront of Tory attacks on Ken Livingstone in March for using a tax loophole to pay 20% tax on his outside earnings. He said to Nick Clegg in the House of Commons: "Last weekend you spoke about the need for a tycoon tax. Can you say whether you would tailor that to include individuals who claim they want to raise tax on the rich and yet set up companies so they only pay 20%, such as Ken Livingstone?"

Harwood was set up in 2005, the year the then chancellor, Gordon Brown, established tax breaks to allow the funding of the British film industry. Hammond became an investor that year after being introduced to the partnership by David Rangeley, a financial adviser who uses the pseudonym "rdrtaxwizard" online.

From company documents it appears that the company borrowed £13.1m from the Bank of Ireland and has spent £2.3m on expenses.

Although his name appears in Companies House documents as a partner in the firm, Hammond has failed to disclose his involvement in the partnership in the MPs' register. The MPs' code of conduct states that "it is the responsibility of members to notify changes in their registrable interests within four weeks of each change occurring".

In a written response to queries, Hammond said there had been a deferral of tax but he believed the scheme complied with tax laws. "I asked and was reassured that the scheme was both entirely legal and HMRC [HM Revenue & Customs] compliant," he said.

Hammond said he had no idea that he was listed as an "associated director" to the company until he was contacted by the Guardian. "This is, of course, incorrect as, by definition and by its legal entity, a partnership has no directors," he said.

He said he believed he was not required to record his partnership in the register of members' interests because he was an investor and not a director, but said he was seeking assurances from "appropriate sources" about whether his assumption was correct.

"As the scheme was a sale and leaseback, by its very nature there was a deferral of tax but there was always a tax liability, which I now declare and pay every year. Therefore as HMRC have never raised a query with me I have always assumed that the advice that the scheme was entirely legal and HMRC compliant to be correct," he wrote. "I have today spoken to Mr Rangeley who has confirmed the HMRC do not believe this to be an aggressive scheme and he will be happy to furnish you with the details of the films Harwood financed."

The minister did not respond to questions about how much and in which films he had invested. Rangeley did not respond to emails.

Hammond has declared a number of other interests in the register including a non-declarable equity stake in Agua Terra, a development company based in the offshore haven of the British Virgin Isles, and shareholdings in Peal Gas, based in the low-tax jurisdiction of Delaware.

Two other Harwood partners have told the Guardian that when they joined the scheme they did so primarily for the tax advantages. One said: "It has allowed me to defer tax, and that has been useful. When it was sold to me by Rangeley he did not mention the films it was going to invest in and I don't know if it ever has."

Simon Danczuk, the Labour MP for Rochdale, has written to the parliamentary commissioner for standards, Sir John Lyons, asking him to investigate whether Hammond has broken the rules.

"The Conservatives talk tough about tax evasion, but it's just lip service. At a time when everyone should be paying their fair share of tax it is morally wrong that Hammond is involved in a scheme that helps the wealthy to avoid paying their share," he said.

Film partnerships became popular as a means of avoiding tax after Brown set up tax breaks for the industry in 2005. Tax officials have launched a push to close film schemes in the belief that some have stepped over the line into aggressive tax avoidance.

In April a tax tribunal ruled that the film partnership Eclipse 35 was an aggressive avoidance scheme. Investors including the football managers Sir Alex Ferguson and Sven-Goran Eriksson were told that investors were not entitled to tax reliefs the scheme had been intended to provide.

Hammond has recently asked a number of written parliamentary questions about tax avoidance and evasion. In September 2011 he asked George Osborne for the estimated monetary rate of tax avoidance and tax planning schemes in force in 2000 and each year since 2005, the year in which he became an investor in Harwood.

A spokesman for HMRC said: "Film schemes are working well as a means of supporting and financing the film industry. But we are cracking down on those schemes that abused the rules."