A rightwing thinktank has been ordered by the charities watchdog to take down a pro-Brexit report on Britain’s economic prospects after it leaves the EU. The report was hailed by Jacob Rees-Mogg as the alternative to Theresa May’s proposals.

The Charity Commission told the Institute of Economic Affairs (IEA) to remove Plan A+: Creating a prosperous post-Brexit UK from its website and stop promoting the report.

A statement from the watchdog said the report had “overstepped the line of what is permissible charitable activity”.

Published in September, it had staunch backing from leading Brexiters including David Davis, Boris Johnson and former Treasury minister Greg Hands. Rees-Mogg, chair of the European Research Group (ERG) of Tory Brexiters, described it as the “most exciting contribution” to the debate in months.

IEA's Brexit proposals: the main points Read more

The report advocated ditching May’s Chequers plan in favour of a Canada-style free trade deal and a new Anglo-Irish agreement to preserve an open border with Northern Ireland. A new law would make it an offence to export to the “Irish market” in breach of the new arrangements.

However, the charities watchdog said its contents were “not sufficiently balanced and neutral as required of an educational charity under charity law. We also found that the charity had been undertaking political activity not in line with the charity’s purposes.”

The Charity Commission’s intervention prompted a robust response from the IEA which said it was “concerned” about the decision, yet agreed to remove the report from its website and stop promoting its contents.

“We believe it is increasingly unclear what charitable thinktank activity is acceptable, and what is not,” said Neil Record, chairman of the IEA board of trustees, who also revealed it was looking at setting up a non-charitable arm.

Play Video 0:53 Jacob Rees-Mogg on vote of no-confidence: 'Patience is a virtue' – video

The saga has caused such consternation to the watchdog, a non-ministerial government department, that it will write to all charitable thinktanks in England and Wales to “remind them of their duties as trustees to ensure that they comply with the law”.

David Holdsworth, the commission’s deputy chief executive, said: “Charitable thinktanks are first and foremost charities and need to behave as such. It is disappointing that the trustees of some charitable thinktanks appear not to fully understand their duties.”

The development is not the first time the thinktank has been the subject of interest from the Charity Commission. In July the Guardian and Greenpeace UK published an undercover investigation into the IEA’s work in the “Brexit influencing game”.

The thinktank had been offering potential US donors access to ministers as it raises funding for research to support the free trade deals demanded by hardline Brexiters.

Greenpeace secretly recorded the IAE’s director, Mark Littlewood, saying it was “in the influencing game” and gave the recording to the Guardian, which in July prompted the Charity Commission to open a regulatory compliance case into the IEA on the basis of concerns about its political independence.

Casino owners donated to IEA after thinktank's pro-gambling report Read more

The IEA strongly defended its position, stating that donations were for research purposes and it made “no apology for seeking to raise funds”.

Greenpeace deputy director Ben Stewart said: “For too long the IEA has wanted to have all the benefits of being a charity without the responsibilities. It seems they wanted to have their cake and eat it.

“The Charity Commission has now told them they can’t. We await with great interest the commission’s report into our investigation.”

The statement from the IEA also expressed concern that the commission was in danger of pushing its powers too far. “A worrying precedent is in the process of being set: research papers – and their launches – which put forward firm policy proposals may now fall outside the parameters of what the Charity Commission considers acceptable activity,” it said .