The Taxpayers' Alliance, a campaign group that calls for tax and spending cuts and claims to represent the interests of taxpayers, has admitted one of its directors does not pay British tax.

The Guardian has learned that Alexander Heath, a director of the increasingly influential free market, rightwing lobby group, lives in a farmhouse in the Loire and has not paid British tax for years.

The admission, made by Matthew Elliott, the TPA's chief executive and founder, is potentially embarrassing for the Conservative party, which has close links to the group that claims to be "the guardian of taxpayers' money, the voice of taxpayers in the media and their representative at Westminster".

At the Conservative party conference in Manchester this week, the TPA's influence was underlined when David Cameron and George Osborne followed its recommendations for freezing public sector pay and capping civil servants' salaries at the level of the prime minister, unless approved by the chancellor.

Senior Labour figures said the admission that a TPA director does not pay British tax "should ring alarm bells" about the group's influence on the debate on tax and spending. The group has also campaigned against green taxes, quangos and town hall pay.

Heath's status emerged from an investigation into the TPA, which also revealed that the group is heavily funded by a group of businessmen and wealthy donors who also back the Conservatives.

"Mr Heath, a retired teacher, has lived in France since marrying his French wife in 1973," said Elliott in a statement. "He is still a British citizen but he is a French taxpayer (where taxes are higher than in the UK!). He is passionate about the Taxpayers' Alliance." Elliott said Heath returned to the UK for about a fortnight each year and owned no property in Britain.

"The least we can expect for an organisation that purports to represent the interests of British taxpayers is that it is run by people that pay British tax," said Jon Cruddas MP, who said he is one of many Labour MPs concerned about the TPA's growing influence.

"When it emerges that one of the directors doesn't [pay British tax], their motivations seem questionable and alarm bells should start ringing for anyone who comes across the TPA."

He said the organisation's backers suggested there was "a revolving door" between Tory donors and supporters of the TPA, although the group denies it is a front for the Conservatives. The TPA's financial backers include Sir Anthony Bamford, the owner of the JCB digger company, and Tony Gallagher, the owner of Gallagher Estates, both Conservative donors, who with 32 other businessmen have donated about £80,000 to the group through the Midlands Industrial Council.

Malcolm McAlpine, the chief executive of contractor Sir Robert McAlpine, said he had also funded the group. David Alberto, a property developer supplies office space to the group near Westminster worth an estimated £100,000 a year.

The campaign group refuses to publish details of its income or a list of donors, but when pressed, Elliott said the biggest single donation was no higher than £100,000 and its annual income from donations was about £1m. It is a rapid rise for a group which filed accounts for 2005 that showed donations of just £67,547.

The TPA's links to the Conservatives include monthly meetings where speakers have included Eric Pickles, the Conservative party chairman, Liam Fox, the shadow defence secretary, and Daniel Hannan, the Tory Eurosceptic MEP who recently claimed the NHS was "a 60-year mistake".