In his new podcast, Unprecedented, Harri said Johnson referred to Gray as "the psycho" or "the total psycho" as she carried out her investigation into lockdown-busting parties in Downing Street.
On the night before her report, Harri said: "There was only a handful of us in the room – I think four or five – a speechwriter, helping to craft what [Johnson] was going to literally say in Parliament, a couple of private secretaries to check on everything, and me.
"And we were struggling to make any progress because he was getting more and more angry, uncharacteristically sweary and cross, the more he thought about the impact of this and what Sue Gray had done to his premiership.
"And at one point where he was literally hysterical, I think in the old days we'd have recommended a slap or a bucket of water thrown over someone, and all I could think of was 'Look, Boris. Boris, look at me. Look at me. Here's what we're going to do. We're going to order a drone strike. We'll take her out. We'll take Sue Gray out. But right now, right now, this very moment, you need to finish a speech that you are giving to Parliament tomorrow'. And your political career depends on that speech. So, if you don't mind, we're going to sit down and finish it'.
"And I think, mad though it was – and just to stress, I was not serious about recommending that course of action – it was the nearest thing I could think of to slap.
"It worked. We sat down, finished the speech in 10 minutes flat and the following day, he did face the parliamentary music."
Johnson this week accused the Cabinet Office of "a politically-motivated stitch-up" after he was referred to the police over entries in his diary relating to visits to No10 and Chequers by his family and friends during lockdown.
It has also emerged that the public inquiry into Covid has gone to war with the Cabinet Office over its refusal to hand over WhatsApp messages between Johnson and other senior political figures during the pandemic.