Britain must suffer the consequences of leaving the EU in order to save the institution from an existential crisis, François Hollande said on Thursday.

Speaking in Paris at a dinner attended by Jean-Claude Juncker, EU commission president, and Michel Barnier, the EU’s top Brexit negotiator, the French president urged the bloc to lead tough negotiations with the UK to avoid contagion and protect the fundamental principles of the single market.

“The UK has decided to do a Brexit, I believe even a hard Brexit. Well, then we must go all the way through the UK’s willingness to leave the EU. We have to have this firmness,” President Hollande told 150 guests at the 20th anniversary of Notre Europe, the pro-EU think-tank founded by Jacques Delors, the former EU commission chief.

“If not, we would jeopardise the fundamental principles of the EU. Other countries would want to leave the EU to get the supposed advantages without the obligations.”

The Socialist leader insisted: “There must be a threat, there must be a risk, there must be a price. Otherwise we will be in a negotiation that cannot end well.”

President Hollande’s warning comes as British Conservative prime minister Theresa May signalled that the UK might be heading for confrontational talks with the EU.

At the weekend, Mrs May said that she would seek to regain control of immigration and refuse to submit to rulings of the European Court of Justice, which would make it difficult for the UK to remain a member of the single market. Amber Rudd, home secretary, caused outcry throughout the continent with a plan for UK-based companies to draw up lists of foreign workers.

Under pressure from a resurgent far-right National Front, which also plans to hold a referendum on the EU if its leader Marine Le Pen reaches power, Paris has been an early advocate of a tougher line towards the UK. A soft Brexit would embolden anti-EU populist parties across the bloc, France has argued.

Berlin has gradually reached the same conclusion, diplomats say. Angela Merkel, German chancellor, has lately hardened her position, warning European business on Wednesday not to press for “comfortable” deals in the Brexit negotiations that could undermine basic single market principles, such as freedom of movement.

On Thursday evening, a normally more diplomatic Mr Hollande did not mince his words. Europe, he noted, “has always lived with crises. But this time, it’s not another crisis. It is the crisis.”

He recalled the time when Jacques Delors, Mr Hollande’s mentor, had to deal with “a crisis triggered by the UK too” as commission president.

“Then Ms Thatcher wanted to stay in Europe, but she wanted a cheque in return,” the French president said. “Now, the UK wants to leave and pay nothing. It’s not possible.”