Mr Cummings, who was still working in Downing Street at the time of the drinks party on 20 May 2020, said the prime minister had been told that it would break Covid guidelines.
He added that he had warned Mr Johnson about the gathering but the PM had "waved it aside".
Mr Johnson said: "I can tell you categorically that nobody said that this was something that was against the rules, that was in breach of the Covid rules."
Two other former Downing Street officials told the BBC they remembered Mr Cummings telling them on that day he had advised the prime minister not to allow the drinks to go ahead.
Be careful. What looked like a Christmas quiz was actually an emergency Cobra meeting to establish which Irish singer-songwriter had a 1990 hit with "Nothing Compares 2 U"