Prime Minister David Cameron

Conservative Jacob Rees-Mogg called for an inquiry into the allegations and warned the Prime Minister faced having to resign if they were true.

Boris Johnson claimed the alleged pact between Mr Cameron and the corporate world over campaigning for Remain “stinks to high heaven”.

It comes after a leaked letter from Rupert Soames, chief executive officer of outsourcing company Serco, to the premier emerged. The missive, seen by the Daily Mail, that was sent on February 8, followed a meeting between the Serco boss, who is the brother of Conservative MP Sir Nicholas Soames, and Mr Cameron.

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It states: “There were two points I thought I might follow up on. The first is how to mobilise corporates to look carefully at the risks Brexit represents.

“I am working with Peter Chadlington and Stuart Rose (the head of Britain Stronger in Europe) with a view to contacting FTSE 500 companies who have annual reports due for publication before June and persuading them that they should include Brexit in the list of key risks. All public companies are required to set out in their annual report an analysis of key risks.”

Updating MPs on the progress of the EU renegotiations on February 3, Mr Cameron said: “Let me say again that if we cannot secure these changes, I rule nothing out.”

Mr Rees-Mogg said: “It’s outrageous, it’s a real scandal because assuming it’s true ... then Parliament was misled and if Parliament was misled then historically it’s led to resignations.”

He told the Bruges Group in central London: “I think to be organising the Remain camp when saying that you’ve ruled nothing out, not just to MPs but to the British people, is shocking and I think we need an inquiry to find out whether this was going on.”