Meanwhile French President Emmanuel Macron’s office said on the eve of his visit to the UK for talks with Theresa May that his country would look with “kindness” on any future British move to reverse its exit from the European Union.
The leaders spoke after European Council President Donald Tusk on Tuesday urged Britain to change its mind and stay in the EU, saying that “our hearts are still open for you”.
European Commission President Mr Juncker, whose team is heading Brexit talks with Britain, told a session of the European Parliament meeting in Strasbourg: “Mr Tusk said that our hand remains outstretched.
“The British people, the British government, may wish to find a different way out of the Brexit situation and we are very much willing to deal with them.
“We are not throwing the British out, we would like the British to stay, and if they so wish, they should be allowed to do so.
“In London, there was a rather irritated response to this proposal (to stay in the EU), but note that even if the British leave according to Article 50, then Article 49 would allow them to accede again and I would be happy to facilitate that,” he said – after initial confusion with the translation suggested he had named Article 94 rather than 49.
Mr Juncker said Brexit was a “lose-lose situation” for Britain and the EU – but admitted the Continent must take some responsibility for the UK referendum vote.
“I still feel the exit of Britain is a catastrophe, yes, a defeat we all have to take responsibility for,” he said in response to a German MEP’s question as to whether Mr Juncker felt responsible.
“But the reasons for the British exit lie deeper.
“As Theresa May has said, the British never felt at ease in the EU and for 40 years they haven’t been given the chance to feel more at ease. That is why the blame is on many.”
In Paris, a key aid to Mr Macron told reporters: “If tomorrow, or the day after, the UK decided to change its mind, it’s clear that we would look at this with kindness.”
However the source added: “But it’s not up to us if the UK wants to change its mind.”
Downing Street insisted in response that Britain will leave the EU in accordance with the 2016 referendum decision.
Mrs May’s official spokesman told reporters at Westminster: “The Prime Minister has been absolutely clear that we are leaving the EU and consequently will be honouring the will of the British people.
“You have seen constructive talks throughout between us and the EU and between the Prime Minister and her counterparts.
“We look forward to that continuing into the next phase of negotiations.
“I think we have been very clear from the outset that we are leaving; that is what the British people voted for. Efforts should continue on working together to build the future partnership.”
Richard Tice, co-chairman of pro-Brexit group Leave Means Leave said: “Jean-Claude Juncker and Donald Tusk need to accept that Britain is a democracy – something the EU knows very little about.”
In Strasbourg, Irish PM Leo Varadkar insisted it would not be “anti-democratic” for British voters to reverse their 2016 Brexit vote in a new referendum.
There have also been renewed calls for a second referendum once an EU deal is done, after former Ukip leader Nigel Farage warned pro-Europeans in Parliament could force one to be held.
Mr Varadkar rejected an accusation by MEP Mr Farage that he was part of a pro-EU plot to thwart Brexit and give Britain the worst possible trade deal even at the risk of harming Ireland’s own commercial links with the UK.
Acknowledging that Ireland had reversed referendum decisions before, Mr Varadkar told reporters in Strasbourg: “I don’t think it’s anti-democratic for anyone to change their mind or have a second vote.
“But any decision on the second referendum must only be one for the UK parliament and the UK people.”
Anti-Brexit Labour MP Chuka Umunna of the Open Britain campaign for close ties with the EU, urged Mrs May to accept that Brexit “on the terms it was sold is not possible, and be honest with people about the huge trade-offs ahead.
“Given what is at stake, everyone is right to keep an open mind about Brexit.”
Contrasting progress so far with the hopes set out by Mrs May a year ago in her “Lancaster House” speech on Brexit, Mr Umunna claimed: “Brexit is proving to be far more costly and complicated than we were led to believe.
“The promises made by the Prime Minister last January are today as worthless as a degree certificate from Trump University.”
January 17th, 2018: Express