The Prime Minister came under pressure over an article in a German newspaper which suggested EU Commission President Jean-Claude Juncker left the meeting last week “10 times as sceptical” about talks succeeding.
Mrs May was branded a “kamikaze” leader for repeating her claim that no deal was better than a bad deal on leaving the EU.
Downing Street said it did not recognise the account of the dinner at Downing Street last Wednesday which appeared in the Sunday edition of the Frankfurter Allgemeine newspaper.
According to unnamed Commission sources, Mr Juncker told the Prime Minister that “Brexit cannot be a success” under her strategy.
The Commission president was reported to have brandished copies of Croatia’s EU entry deal and Canada’s free trade deal which runs to 2,000 pages in a bid to underline the complexity of the talks ahead.
The Prime Minister was said to have angered the EU side by warning that the UK could not be forced to pay a “divorce bill” for leaving because there was no requirement under the treaties. Mr Juncker is reported to have replied that the EU was “not a golf club”.
As he left, Mr Juncker was said to have told Mrs May: “I leave Downing St 10 times as sceptical as I was before.”
The following morning he rang Angela Merkel to warn her that Mrs May was in a “different galaxy” on Brexit, prompting the German chancellor to tell parliamentarians in Berlin that the UK had “illusions” about the kind of deal it would get.
The Scottish Government’s Brexit minister, Michael Russell claimed the report laid bare Mrs May’s “weak and chaotic” leadership on Brexit and warned of a “looming catastrophe”.
He said: “Having seen first-hand how the Tories negotiate on EU matters, I am frankly not surprised by anything reported here.
“Behind the façade and the robotic sound-bites the Tories are quite clearly not being straight with people about their plans for Brexit.
“This looming catastrophe shows precisely why Theresa May mustn’t be allowed to block the decision of the Scottish Parliament to give people in Scotland a choice over their future when the terms of Brexit are clear.”
Mr Russell added that leaving the EU without a deal would be an “unprecedented act of self-harm which would devastate the UK and Scottish economy”.
He said: “It is absolutely essential that we have a strong opposition at Westminster who can hold this kamikaze Tory leader to account and put the Brexit talks under real scrutiny.
Jeremy Corbyn accused Mrs May of conducting “megaphone” diplomacy with the EU by suggesting that its 27 members would gang up on the UK.
Campaigning in Battersea, south London, the Labour leader claimed Mrs May’s negotiating strategy was unravelling.
“To start negotiations by threatening to walk away with no deal and set up a low tax economy on the shores of Europe is not a very sensible way of approaching people with whom half of our trade is done at the present time,” he said.
“Of course [negotiations] are going to be difficult, but you start from the basis that you want to reach an agreement, you start from the basis that you have quite a lot of shared interests and values.
“If you start from that basis and show respect, you are more likely to get a good deal. But if you start with a megaphone, calling people silly names, it is not a great start to anything.”
Liberal Democrat leader Tim Farron said the report suggested the government was taking the UK towards a “disastrous” hard Brexit.
Mr Farron said: “Theresa May’s lack of denial suggests these damning revelations about her approach to Brexit were largely accurate.
“This government is showing dangerous levels of complacency over an issue that will define our country for generations.
“Britain desperately needs a strong opposition to stop a catastrophic hard Brexit and hold this government to account.”
Campaigning in Ormskirk in Lancashire, Mrs May brushed off the claims insisting that they were at odds with what the commission had said about the meeting.
“From what I have seen of this account, I think it is Brussels gossip,” she said.
“Look at what the European Commission themselves said immediately after the dinner took place which was that the talks had been constructive.”
The Prime Minister added: “When it comes June 8 people have a clear choice.
“There will be 27 European countries on one side of the table - who do they want to see standing up for Britain on the other side? Me or Jeremy Corbyn.”