The Defence Secretary and South Staffordshire MP was reported to have been overheard discussing his chances of succeeding Theresa May during a plush dinner at exclusive Mayfair restaurant The Colony Grill.
A national newspaper reported that he was heard boasting about his links with the DUP, and how he could outmanoeuvre Foreign Secretary Jeremy Hunt and Home Secretary Sajid Javid in the next Tory leadership contest.
But allies of Mr Williamson have defended him, claiming a senior party figure has embellished an eavesdropper's account of a private conversation to make it sound as though he was plotting against his Cabinet colleagues.
On the night in question Mr Williamson was dining with James Wharton, a former Tory MP, and one of Mr Wharton's friends who he had never previously met.
Former International Development Secretary Mr Wharton, who lost his seat in 2017, said: "Gavin had to stay late for a vote so he texted me to see if I was around for dinner.
"I said I was though I had a friend with me, and the three of us went for a meal. My friend has no interest in politics so we tried to avoid the topic as much as possible.
"It's utter rubbish to suggest he was somehow plotting or discussing his chances of becoming leader, especially as my friend was a total stranger to him.
"Whatever this other person heard has been wildly embellished.
"The reason I'm friends with Gavin is that my name comes after his alphabetically so we were next to each other when we became MPs.
"If he was plotting something I think he would choose someone rather more influential than me. It seems to me a bit of a hatchet job."
A source close to Mr Williamson is reported to have said: "He is furious about this. Gavin does not have leadership ambitions, he wants to stay as Defence Secretary to complete what is a very important job."
Bitter rows between Cabinet ministers have intensified since Mrs May announced she would not fight the next General Election.
The Prime Minister's leadership can't be challenged by her own party for the next 12 months after she won this month's leadership contest that was sparked by dissatisfaction over her Brexit deal.
Meanwhile allies of Mrs May are said to believe they can keep her in position until 2021 – a year before the scheduled date for the next election – giving her enough time to clear out the Cabinet old guard through multiple reshuffles.
Senior figures who have discussed the plan want her to hand over the keys to Number 10 that summer, giving the new Prime Minister around nine months to prepare their new team before voters head to the polls.
Favourites to take over from Mrs May include Mr Javid, ex-Brexit Secretary Dominic Raab and International Aid Secretary Penny Mordaunt.
The succession plan is likely to cause uproar among Eurosceptics, who want Mrs May to leave shortly after the UK formally departs the EU in March next year.
One Brexiteer Tory MP said: “The PM must go as soon as practically possible after we leave the EU.
“We don’t want her or her advisers working on the future trade deal with the EU. It just can’t happen.”
Mrs May has cut short her Cabinet ministers’ Christmas break, summoning them to a meeting to discuss a 'no-deal' Brexit on January 2.
Senior Tory officials have expressed growing confidence that Mrs May’s Brexit deal will pass the Commons next month, although they see it as an attritional struggle that may involve the bill being defeated on the first and even second attempt.
Her tactics now appear to hinge on winning over the DUP and maximising the threat of a 'no-deal' Brexit.