Civil servants may be secretly distorting evidence to “influence” the Government to stay in the EU’s customs union, a Brexit minister has suggested.

Steve Baker floated the conspiracy claim on the floor of the House of Commons, telling MPs he did not necessarily believe it – but did not rule it out.

“I think it would be quite extraordinary if it turned out that such a thing had happened,” the hard Brexit supporter said.

Mr Baker said he “considered it implausible” when the allegation was put to him by the head of an influential think-tank on EU policy.

But he added: “What I would say is we need to proceed with great caution, because it is essential we continue to uphold and support the impartiality of the civil service.”

The comments blindsided Downing Street, which said it was unaware that the allegation had been aired and declined to comment on it immediately.

Alongside Mr Baker, his boss – the Brexit Secretary David Davis – visibly winced as the minister confirmed the allegation, raised by his fellow anti-EU Tory, Jacob Rees-Mogg.

Meanwhile, the think-tank head who spoke with Mr Baker - Charles Grant, of the Centre for European Reform – flatly denied he had made any allegation about a civil service conspiracy.

Mr Baker spoke out amid fury over the leak of secret Brexit analysis, now to be released to MPs, which concluded the UK will be poorer under all mooted exit options.

Brexit: the deciders Show all 8 1 /8 Brexit: the deciders Brexit: the deciders European Union's chief Brexit negotiator, Michel Barnier Getty Brexit: the deciders French President Emmanuel Macron Getty Brexit: the deciders German Chancellor Angela Merkel Reuters Brexit: the deciders Commission President Jean-Claude Juncker EPA Brexit: the deciders The European Parliament's chief Brexit negotiator Guy Verhofstadt Getty Brexit: the deciders Britain's Prime Minister Theresa May Getty Images Brexit: the deciders Britain's Chancellor of the Exchequer, Philip Hammond PA Brexit: the deciders After the first and second appointed Brexit secretaries resigned (David Davis and Dominic Raab respectively), Stephen Barclay is currently heading up the position PA

Brexiteers have privately accused the head of the civil service of conspiring with the Treasury to produce the devastating research, without the knowledge of ministers in the Department for Exiting the European Union (DExEU).

However, during the same question time in the Commons, Mr Davis revealed he had known the research had been commissioned two months’ ago and that it was discussed by ministers earlier this month.

The controversy blew up when Mr Rees-Mogg asked Mr Baker to confirm that Mr Grant had told him that “officials in the Treasury have deliberately developed a model to show that all options other than staying in the customs union were bad and that officials intended to use this to influence policy”.

Mr Rees-Mogg added: “If this is correct, does he share my view that it goes against the spirit of the Northcote rebellion reforms that underpin our independent civil service?”

Mr Baker replied: “I am sorry to say that my honourable friend's account is essentially correct.

“At the time, I considered it implausible because my direct experience is that civil servants are extraordinarily careful to uphold the impartiality of the civil service.

“I think we must proceed with great caution in this matter but I heard him raise this issue.”

Challenged by Opposition MPs, Mr Baker added: “I didn't say it was correct. I said the account that was put to me is correct. It was put to me. I considered it an extraordinary allegation. I still consider it an extraordinary allegation."

But, speaking soon afterwards, Mr Grant said he had simply passed on that he had heard Treasury forecasting had shown free trade agreements would fail to compensate for the economic costs of leaving customs union.