The Conservative party treasurer is calling for a major change in tax laws so that Britain can compete with offshore havens.

Lord Fink, the Tory donor and hedge fund chief, disclosed in an interview that he had lobbied George Osborne for a cut in taxes on invisible earnings so that he and other hedge funders no longer feel obliged to set up companies in places such as the Cayman Islands.

His comments came as a Guardian investigation reveals that 68 MPs and peers, who can influence Britain's tax laws, are either directors or non-executive directors of firms linked to tax havens.

The findings show how widespread the use of offshore jurisdictions has become in British business life – even by companies which have lawmakers and major public figures on their boards.

Politicians and companies have claimed that many of the offshore firms are established in these jurisdictions for operational business functions or administrative reasons rather than to secure a lower tax liability.

Fink, who is a director of three firms which have subsidiaries or a parent company in the Cayman Islands, Luxembourg and Guernsey, said: "I don't see why the UK should not compete for jobs that at present are going to the Cayman Islands. I lobbied George Osborne when the Tories were in opposition. I have long felt that the British government loses jobs to tax havens by allowing the Revenue to have these rather archaic rules."

The new business minister, Michael Fallon, the former trade secretary Peter Lilley and the backbencher Jacob Rees-Mogg are among six Tory MPs who are listed as officers of firms established in, or linked to, jurisdictions known for opaque practices and low tax.

Sixty-two peers including the Tory peer and composer Lord Lloyd-Webber, the former Lib Dem business spokesman Lord Razzall and Labour's Lord Carter of Coles are also involved with businesses that have offshore connections. Lloyd-Webber's company said its offshore subsidiary was dormant. Razzall said his company, which offers services including tax mitigation to clients, had not indulged in aggressive avoidance. Lord Carter has not responded.

Of the 68 parliamentarians who have links to offshore havens, 27 are Tories, 17 are Labour peers, three are Lib Dem peers and another 21 are either crossbench or non-affiliated peers.

The Guardian examined the registers of MPs' and lords' interests to identify companies where they are registered as directors or non-executive directors. This information was cross-referenced with accounts or other financial records to find out if the companies were registered or had a parent company or subsidiary in a tax haven.

Revenue & Customs does not provide a list of tax havens. The Guardian has drawn upon a list of 35 jurisdictions identified for their secrecy and low tax compiled for the US Congress in 2009.

The findings follow a national debate over the use of tax loopholes, prompted by claims from Osborne and David Cameron that they will clamp down on loopholes that allow "morally repugnant", albeit legal, aggressive tax avoidance. Anger at tax avoidance was heightened after revelations about the tax affairs of celebrities including the comedian Jimmy Carr.

Legal tax avoidance represents nearly 14% of the UK tax gap, according to the Treasury. Research commissioned by the campaign group Tax Justice Network has found that at least £13tn of wealth has been hidden offshore.

Of the parliamentarians identified, most claimed the offshore firms were not being used for tax or corporate purposes. Many of the politicians and companies also said they made large tax contributions in the UK.

Margaret Hodge, who chairs the Commons public accounts committee, which is conducting an inquiry into tax loopholes, said the findings were worrying because of the lack of transparency in offshore havens.

"As MPs, these individuals should be voting for proper transparency so we can see that these companies pay proper tax in the UK. The number of peers involved is bad enough. But to find that Tory MPs are setting themselves up as non-executives on companies that are connected to these places where there is such a lack of scrutiny and probity is just reprehensible and beyond belief," she said.

Fallon was until two weeks ago a non-executive director of Tullett Prebon, the international money brokers. He stepped down when he took his post in the reshuffle. In 2008, he criticised Gordon Brown over the nationalisation of Northern Rock after it emerged the bank had a subsidiary in a tax haven. Under Fallon's directorship, for which he was paid £51,000 a year when he left, Tullett also had an offshore operation in Guernsey. Tullett is registered in England, but it owns subsidiaries in secretive, low-tax jurisdictions including the Channel Islands, Switzerland and, until last year, Bermuda. He stood down as chairman of Tullett's remuneration committee in 2009 after an outcry over the company's decision to offer help to move staff to countries with more favourable tax regimes after the announcement of a tax on City bonuses.

Fallon said none of Tullett's subsidiaries in Guernsey, Jersey and Switzerland were set up for tax reduction purposes and that the Guernsey and Jersey companies were resident for UK tax. The company said its Swiss arm was serving customers there and that Tullett had achieved HMRC's "low risk" status.

Rees-Mogg declares his directorship of three separate companies related to Somerset Capital Management LLP on parliament's register of financial interests. However, he says he is not required to declare Somerset Capital Management (Cayman) Ltd (SCMC), which he also controls with two other directors, because it has no turnover or profit and the UK company receives all its revenue. "I do not believe people have any obligation to pay more tax than the law requires but SCMC has no tax benefit to me, Somerset Capital Management or to our clients," he said.

Tony Baldry, the Conservative MP for North Oxfordshire, was awarded a knighthood in the Queen's birthday honours. On a £64,000 salary, he acts as an independent non-executive director at Woburn Energy whose parent company is registered in the British Virgin Islands tax haven. He said the company was independent from its parent, Cetus, and the offshore links were "entirely as a consequence of the ownership structure of Cetus prior to its investment in Woburn".

Peter Lilley was recently appointed non-executive chairman of Tethys Petroleum, which has interests in Kazakhstan, Tajikistan and Uzbekistan. The company is registered in the Cayman Islands.

He said: "Tethys would not have a UK tax liability if it migrated to the UK since, as an exploration company, it reinvests its revenues in exploration, which extinguishes any tax liability under UK tax law. It of course pays taxes, royalties and production share to local governments in countries where it operates."

The Tory former defence minister Nicholas Soames is chairman of private security contractor Aegis, owned by a Swiss holding company and with subsidiaries in the British Virgin Islands. Soames said: "All trading profits of the group are either paid to or taxed as part of Aegis Defence Services Ltd's own activities and that company is fully taxable in the UK."

Jonathan Evans, MP for Cardiff North, is non-executive chairman of Phoenix Life Ltd. Accounts from Companies House show Phoenix's parent company is incorporated in the Cayman Islands and resident in Jersey. Evans did not respond to questions about the company.

Comments will be turned on at 8am on 21 September 2012

• This article was amended on 21 September 2012 because the original said Michael Fallon moved from chairman to non-executive director of Tullett Prebon in 2009. Fallon has never been the company's chairman; the post he stood down from in 2009 was the chairmanship of its remuneration committee.