Civil servant Ms Gray is heading an inquiry investigating the Downing Street parties during lockdown which has been dubbed “partygate”.
Her report is set to be published this week.
Now the Prime Minister’s former aide revealed he had submitted written evidence and would be willing to answer further questions in writing.
On his blog, Mr Cummings said: “When SG [Sue Gray] asked to speak to me I emailed to the effect: if we speak the PM will invent nonsense and spin it to the media and you and I will both have problems, let’s keep everything in writing, therefore he cannot invent things I’ve supposedly said to you, there is only a written record, this makes both our lives easier.
“She agreed. So I have answered questions in writing and will answer further questions in writing if she wants.
“But I will not speak and therefore provide the PM with more chances to lie and confuse everybody.”
Mr Cummings made further claims further evidence, including photos, would continue to leak into the public domain after Ms Gray’s report.
“I know others are very worried about handing things to the Cabinet Office because they know the PM will see everything SG collects,” Mr Cummings said.
“This inevitably means that evidence, including photos, is not given to her and instead will keep leaking after her report. (To stress, this is a consequence of beliefs about the PM’s integrity, not SG’s.)
“Other damaging stories will come out until he is gone.”
Elsewhere on Monday, Mr Johnson said people had to “wait” for Ms Gray’s report when asked about it by reporters.
Speaking at an Academic Centre at Milton Keynes Hospital in Buckinghamshire, the Prime Minister said: “I perfectly understand you want to ask questions about that but you’ve got to wait for that to come.
“But what I will say is this Government is focused on the stuff that I think people want us to focus on.
“And we’ve come through Covid faster than most other European countries thanks to some of the decisions we took, thanks to our incredible NHS, thanks to what they did with the booster rollout and the unbelievable work that they did – and the British people who followed the advice and have delivered the result that we’re in.”