The prime minister had previously denied the allegation, but in an interview with ITV News Political Correspondent Paul Brand, he said he has no recollection of ever attending the event in question.
When asked if he could remember the event, Mr Johnson responded: "All I know is it is not true."
When pressed, the prime minister conceded, "to be honest, I have no memory whatever".
Video report by ITV News Political Correspondent Paul Brand
He added: "It is not true, for all sorts of reasons, and I don’t wish, as I say, to minimise the importance of the subject, I don’t wish to, you know, cast aspersions on the motives of anybody who makes this type of allegation but it is not true and what I want to do is focus on our domestic agenda."
He defended his time in City Hall and said he won't allow allegations to "knock the government off course" from its "vital mission" of delivering Brexit by October 31.
Paul Brand said: "But even he turns back into a sensitive scientist."
Mr Johnson agreed, saying he would be "proud to be compared to Bruce Banner the nuclear physicist".
ITV News Political Editor Robert Peston with the latest from the party conference
"I’ve been tasked with getting Brexit over the line in a time of national controversy. There is no way of fudging it. You can’t be half in and half out of the EU, you can’t be 52% out and 48% in, it just doesn’t work," he said.
Asked if he had a softer side, the PM said: "Of course - I don’t know what you mean exactly by that, but I suppose yes."
Watch the full interview here: