The new minister for securing the UK’s departure from the EU is under pressure to clarify his relationship with the obscure organisation behind a controversial £435,000 donation to the Democratic Unionist Party during last year’s Brexit referendum.

Steve Baker, a leading light on the Tory right, has also received £6,500 from the Constitutional Research Council, the body behind the DUP donation. The revelation has heightened interest in the council and its links to two powerful organisations now holding sway over British politics: the DUP, whose 10 MPs are propping up the Tory government, and the European Research Group, an increasingly influential group of around 80 pro-Brexit MPs that was chaired by Baker until he stood down last month.

The council is chaired by Richard Cook, a former vice-chairman of the Scottish Conservative and Unionist party, whose business associates include a former Saudi spy chief and a man alleged to have been an intermediary in a major arms scandal. It has no website and publishes no accounts and is one of several organisations that have emerged as having played a key role in securing Britain’s exit from the EU.

In his register of interests, Baker states: “As chair of the European Research Group (ERG), I accepted £6,500 from the Constitutional Research Council to fund hospitality for ERG members and their staff at an event on 19 December 2016.” Baker’s promotion in Theresa May’s recent reshuffle was seen in Conservative circles as proof that the Tory right was now the dominant force in the party.

The Observer approached Baker to ask whether he was confident that he knew the identity of all the council’s members and donors. Questions to his office were referred to Department for Exiting the European Union, the ministry charged with Brexit. A spokeswoman for the department said she was unable to answer the question. The Observer was told to contact Christopher Howarth, the senior researcher for the ERG. Howarth said: “It’s a registered donation from a permissible donor. That’s all the information you would need.”

Labour MP David Lammy, a staunch opponent of Brexit, said: “This smacks of House of Cards. I’m afraid with all that’s going on in the US with Donald Trump’s campaign we need to understand what interests have been keen to support Steve Baker now he’s in this crucial role.”

Richard Cook, the chairman of the Constitutional Research Council, which has no website, publishes no accounts and is not obliged to reveal its donors. Photograph: Universal News And Sport (Europe)

Sir Vince Cable, the Lib Dem MP and former business secretary, said: “It’s a scandal that this is shrouded in secrecy. We must know who the donors are and the fact that the DUP have such a prominent role in British public life means that these obscure transactions can no longer be hidden in Northern Ireland.”

Under rules drawn up during the Troubles, parties in Northern Ireland, unlike the rest of the UK, are not obliged to reveal the identity of their donors, for security reasons. But Blair McDougall, a former Labour candidate who, like Cook, has contested the Westminster seat of East Renfrewshire, said “it’s unsustainable not to reveal the source of the money now that the DUP are in power.”

It was only after campaigning journalists at Open Democracy started asking questions that the DUP caved in and named the CRC as the organisation that had given it the huge donation.

Lord Bew, chairman of the Committee on Standards in Public Life, said a change to bring greater transparency to Northern Ireland’s party finance laws was long overdue.

“Given the high degree of public scepticism about the motivations of donors and recipients in party political funding, the committee regards transparency as a foundation block in maintaining public confidence across the political system,” he said. “We called on the government to commit to a timetable for bringing transparency arrangements in Northern Ireland into line with those in the rest of the UK as part of our package of recommendations in 2011. We welcomed the recent consultation on these issues; like many aspects of party funding reform, we believe they have been left in the ‘too difficult’ pile for too long.”

The CRC is not obliged to reveal its donors. Many unincorporated associations have for years made donations to all the main political parties without making declarations.

But Robert Barrington, executive director of Transparency International UK, said the law needed changing. “This is a sordid, but sadly not unusual, little tale of people in positions of power deliberately exploiting the loopholes around political donations,” he said. “The loopholes should be closed, there should be full transparency over the donations in question and the rules in Northern Ireland should at last be changed.”

Cook, like Baker, has been a supporter of the Freedom Association, the organisation founded by a group of Tory MPs alarmed by the rise of trade unions and Irish republicanism. In the 1980s the Freedom Association campaigned for the right of England cricketers to tour apartheid-era South Africa.

In 2012 his company, Cook Consulting, signed agreements to deliver environmental projects in Karachi worth more than £600m.

Arlene Foster, the leader of the DUP, which received £435,000 from the Constitutional Research Council. Photograph: AFP/Getty Images

But where the CRC gets its money from is a mystery. Cook, who did not respond to requests for comment, has said “three or four individuals” donate. In May he explained to the Sunday Herald in Scotland how the CRC decided who to fund. “People come to us with projects [and] they tell us how it is promoting the Union. The executive committee assess that and will decide.”

Cook is unlikely to be a substantial donor. Cook Consulting was dissolved without filing accounts. Five Star Investment Management, a company that he founded with a Dane called Peter Haestrup and whose shareholders included the late Prince Nawwaf bin Abdul Aziz al-Saud, a former director general of the Saudi intelligence agency, has also been dissolved.

Haestrup was named in an investigation into an arms scandal in 1995. Hundreds of AK-47s, anti-tank grenades, pistols and rocket launchers were dropped from a transport plane into West Bengal in what the Indian authorities described as “the biggest crime in the country’s history”. Haestrup was never charged with any offence.

The DUP was asked a series of questions by the Observer, including whether it knew the identities of everyone behind the CRC. A party spokesperson said: “The Electoral Commission has raised no issues in relation to the DUP campaign, including the donation which came from a permissible donor, who in turn are themselves regulated by the Electoral Commission.”

Of the £435,000 given by the CRC to the DUP, only £10,000 was spent in Northern Ireland. Nearly £300,000 was spent on a wraparound pro-Brexit supplement for the Metro newspaper, published in mainland Britain but not in Northern Ireland.

Matthew Oakeshott, a prominent campaigner for the reform of party funding, said: “It’s an outrage – the DUP pick the British PM but make donations in dark glasses through a loophole in our election law.”