In an interview with the BBC's Panorama - recorded in May, before the start of the Conservative leadership contest - the EU's chief Brexit negotiator was asked if the Prime Minister or her team ever mentioned or threatened a no-deal exit.
He replied: "No, no, I never listened to such a sentence. Never.”
Mr Barnier said he believed the UK knew the EU would not respond to threats of a no-deal.
"I think that the UK side, which is well-informed and competent and knows the way we work on the EU side, knew from the very beginning that we've never been impressed by such a threat. It's not useful to use it.”
He added: "We have put in the document (the Withdrawal Agreement) with the UK - not against the UK, with the UK - the legal answers to each and every point of uncertainty created by Brexit.
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"That is the point.”
A Number 10 spokesperson issued a particularly sarcastic response to the claims by Mr Barnier, saying: “Can I begin by saying how nice it was to hear from Michel Barnier again this morning, and how generous it was of the BBC to give him a platform to share his views with us all.
“On that specific point, the Prime Minister was clear, both in public and in private that the UK was prepared to leave without a deal.”
Brexit Party leader Nigel Farage was more direct, saying: “If he [Michel Barnier] is correct then May has openly lied to the British people and betrayed the Brexit vote.”
Darren Grimes, who founded the pro-Brexit campaign group BeLeave, said of the claims: “Turns out that saying one thing to your electorate and something totally different to those around the negotiating table doesn’t actually get you very far. Who’d have thought it?”
Turns out lads that saying one thing to your electorate and something totally different to those around the negotiating table doesn’t actually get you very far. Who’d have thought it? https://t.co/bPvrxJvOJy
— Darren Grimes (@darrengrimes_) July 18, 2019
Mr Barnier, who insisted the Withdrawal Agreement was the only way to leave in an "orderly manner", said the UK would have to "face the consequences" if it walked away without a deal at the end of October.
Boris Johnson, the favourite to take over as PM next week, has vowed to leave the EU with or without a deal by the time of the Halloween deadline.
But the European Commission's top official, Martin Selmayr, told Panorama the UK was unprepared to leave without a deal.
He said: ”We have followed the British debate and the British preparations very, very closely and we have seen what has been prepared on our side of the border for a hard Brexit - we don't see the same level of preparation on the other side of the border.
"You would have to establish a lot of authorities in the United Kingdom that you don't have at this moment in time so I think the European Union have been very well-prepared for that - we could live with a hard Brexit.
"We don't think the same level of preparation is there on the UK side.”
David Lidington, the de facto deputy prime minister, also told the programme that the EU offered to put Brexit on hold in 2018 for five years and proposed a "new deal for Europe”.
He said: "Martin (Selmayr) sort of said 'Look, why don't we have a deal whereby we just put all this on ice for five years? ... Let's see how things go, let's get the UK involved with France and Germany, let's see how the dust settles and let's talk about whether we can come to a new deal for Europe’."