Brexiters have been left “flabbergasted” by the EU’s refusal to back down in divorce talks because the UK has never understood that the single market is seen as vital to the political, as well as economic, stability of the continent, according to the European commission’s vice-president.

Frans Timmermans also expressed the hope that the UK might yet change its mind on Brexit now it “has seen the facts”. There had been no intention to humiliate Theresa May at the recent Salzburg summit, he said.

But he added that the British prime minister had no reason to be surprised by the EU negotiating stance since “she had been told time and time again” by the chief negotiator, Michel Barnier, that her Chequers proposals were unacceptable.

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His remarks, emphasising the threat to the EU’s integrity posed both by Brexit and by eastern European countries challenging liberal democratic values, underline the extent to which some senior European politicians are uninterested in a technical fix, seeing the talks as a battle to defend wider values.

Speaking at Columbia University in New York, he said: “One reason we have so many misunderstandings in the talks is that in the UK from the very start participating in the EU was purely an economic issue – a common market. So therefore when they started negotiating with the rest of Europe they thought, ‘Common market, they are not stupid. If we have a hard Brexit, the German car industry etc will be hit. They will back down.’ That was the fundamental flaw in the thinking of the Brexiteers.”

He added: “In London people were completely flabbergasted that the German car industry did not demand of Mrs Merkel that she should give in to all the demands of the British government.”

He argued: “The German car industry has a clear vision of the necessity of stability in the continent that goes beyond selling cars. For Germany the economy is an instrument in a much wider issue of stability in continental Europe and overcoming the mistakes of the past.”

Discussing the rebuff to the British at the recent summit in Austria that saw EU leaders spell out their refusal to accept the British proposals drawn up at Chequers, Timmermans said: “I can tell you from the bottom of my heart that no one in Salzburg wanted to humiliate Theresa May – there was nothing like that on the table. I can also tell you that what was said about Chequers in Salzburg had been said time and time again to the Brits by Michel Barnier and others. So it should not have come too much of a surprise to her.”

Admitting some of the remarks by EU politicians at the end of the summit could have been more sensitive to British feelings, he held out the hope that the UK might yet rethink its plan to leave, saying “nothing had made me sadder in my last 30 years of my political and diplomatic career than Brexit”.

He said Brexit was a sovereign decision of the British, before asking: “Who in this hall has never ever changed their minds about anything? Is it not in human nature sometimes, based on the facts that you now know, to reconsider? Let me dream.”

But he insisted if the EU did not stand up for itself and defend itself, “those who want to destroy it will have the upper hand” .

Timmermans has been leading the commission’s challenges to the slide away from liberal democracy by Hungary and Poland, and warned of the dangers of nominal democracies of the kind seen in Germany in the 1930s. He said that cases such as Brexit raised fundamental issues about the survival of the EU.

The EU has begun new infringement proceedings under article 7 against Poland for restructuring its supreme court by lowing the retirement age to 65 and so removing a group of judges.

The commission has asked the European court of justice to make an interim ruling to postpone the removal of judges, including the president of the supreme court.

Timmermans said: “One of the principles upon which the EU is built is the separation of powers and the independence of the judiciary.”

He said: “What we did we learn from these two suicidal wars that Europe engaged in during the 20th century? That you can use democracy as a tool to simply ignore human rights or the rule of law: ‘I won the vote so I decide.’ That is very much of part of European history. None of the people killed in Germany was killed illegally. It was all done according to their law book.”

He accepted migration, and fears about identity had created “a political crunch time” across Europe.

“If Europe does not understand that our sister continent, Africa, a stone’s throw away, is going to face a demographic explosion, if there is no real economic and political restructuring, if we do not understand we have a collective responsibility for Africa, there is not a fence high enough to stop people coming to Europe.”

He said surveys showed 50 % of young Nigerians see their future in Europe. He explained: “We are talking about hundreds of millions of people. We need these people to see their future as in Africa. The international contract we need to close with Africa is of the same magnitude and importance as the reconciliation between France and Germany after the second world war.”