The email pushing back on Mr Reynolds’ invitation could complicate Downing Street’s defence because it suggests there was some opposition internally.

However, given that the message appears to have been sent to Mr Reynolds rather than Mr Johnson, it may not categorically undercut the Prime Minister’s defence.

ITV News reported on Thursday that Ms Gray had obtained the email. The Telegraph understands the former Number 10 official directed her to where to find it. How Ms Gray is approaching the investigation, and what format the publication of her findings may take, remains unclear.

Mr Johnson let slip at Prime Minister’s Questions on Wednesday that the report is not due to be published until “next week”.

MPs await report before deciding next moves

Downing Street figures say they are keen to see the report published as soon as possible. However, the timing is up to Ms Gray, who once oversaw proprietary and ethics in the government.

The terms of reference say only that she will reveal her “findings”, meaning detailed descriptions of each event are not expected to be revealed.

One source with knowledge of the investigation’s progress said: “I don’t think people should reasonably expect to see a blow-by-blow ‘at five minutes past one these people pulled out a bottle of wine’ description of events.”

But the fact that Ms Gray is overseeing the investigation rather than Simon Case – the UK’s most senior civil servant personally appointed by Mr Johnson, who was originally in charge – adds uncertainty to the process.

Scores of Tory MPs weighing up their support for the Prime Minister have privately said they are waiting for the report to be published before making a decision on whether to submit a letter of no confidence.

A profile of Ms Gray, published by Politico, had some figures praising her formidable reputation. One former government aide who clashed with her said: “She makes Robespierre look like a choirboy.”

But others were critical. One former adviser said: “Her nickname is ‘Sue Gray area’ because everything she does is so murky. There’s never any paper trail. There’s never any record.” The person, who was not named, added: “Her job is just to make bad things go away for the Prime Minister however she can.”

A Cabinet Office official who works with Ms Gray was also quoted in the article, saying she was “someone of high integrity”.