Charlotte Edwardes, the assistant editor of The Sunday Times, wrote in a column for the daily that Johnson - who was the editor of the Spectator magazine at the time - grabbed "enough inner flesh beneath his fingers" to make her "sit upright".
She claimed that he did the same thing to another woman at the same function.
"More wine is poured; more wine is drunk. Under the table I feel Johnson's hand on my thigh. He gives it a squeeze," Edwardes wrote.
"His hand is high up my leg and he has enough inner flesh beneath his fingers to make me sit suddenly upright."
She said that her usual reaction would have been to confront Johnson, but she stayed silent as it was a "work situation".
Downing Street initially declined to comment, but after senior Ministers were questioned repeatedly about the claim a No 10 spokesperson said: "The allegation is untrue."
When Johnson was asked whether the allegation made by Edwardes was true, he said: "No, and I think what the public want to hear is about what we are doing to level up and unite the country."
On Monday, UK Chancellor Sajid Javid repeatedly refused to discuss any details of the allegation or whether it should be investigated.
"I've talked to the Prime Minister about that. And first of all, he couldn't be clearer, absolutely clear, that (the claims) are completely untrue. I totally trust him on that," he told BBC Radio 4's Today programme.
On Sunday, Health Secretary Matt Hancock told Channel 4 News of Edwardes: "I know her and I know her to be trustworthy."
Amber Rudd, the former Work and Pensions Secretary who resigned earlier in September, later tweeted: "I agree with @MattHancock."
( With inputs from IANS )