Britain and the EU appear more bitterly divided over Brexit than at any time since the referendum, with European leaders ramping up their rhetoric after Theresa May signalled she would seek a clean break with the bloc.

The prime minister’s Conservative conference speech, in which she indicated Britain would prioritise immigration control and restore the primacy of UK law to become an “independent, sovereign nation” without full access to the single market, drew a sharp response from continental capitals.

In Paris, François Hollande said Britain must suffer the consequences of its decision. “The UK has decided to do a Brexit. I believe even a hard Brexit,” he said. “Well, then we must go all the way through the UK’s willingness to leave the EU. We have to have this firmness.”

If not, “we would jeopardise the fundamental principles of the EU”, the French president said on Thursday night. “Other countries would want to leave the EU to get the supposed advantages without the obligations … There must be a threat, there must be a risk, there must be a price.”

Hollande’s message was underlined on Friday by the president of the European commission, Jean-Claude Juncker, who said the 27 remaining member states must not give an inch in exit negotiations. “You can’t have one foot in and one foot out,” he said. “We must be unyielding on this point.”

Britain risked “trampling everything that has been built” over six decades of European integration, he said.

In Berlin, Angela Merkel rammed home the same point. “If we don’t insist that full access to the single market is tied to complete acceptance of the four basic freedoms, then a process will spread across Europe whereby everyone does and is allowed what they want.”

Merkel called on German industry leaders to back the government’s line in Brexit talks, even if it hit their profits. “We have to make sure our interests are coherent here so that we won’t be put under pressure constantly via European industry associations to eventually allow full access to the internal market even if all freedoms aren’t respected,” she said.

The British government has yet to confirm what kind of future relationship it will seek with the EU, but the conditions set down in May’s speech – in particular migration controls on EU citizens and the insistence that Britain will no longer be under the jurisdiction of the European court of justice – effectively rule out membership of the single market.

That will be hard to square with the prime minister’s determination for British firms to have the maximum opportunity to operate within the single market.

In an interview with the Guardian, Joseph Muscat, the prime minister of Malta, which will hold the EU’s rotating presidency when Britain triggers article 50 early next year, said the four freedoms – the movement of goods, capital, services and people – could not be decoupled. “That cannot be negotiated … These principles are the basis for everything the EU does,” he said.

The French finance minister, Michel Sapin, said on Friday that eurozone governments would not accept the City of London remaining the main euro clearing centre once Britain left the EU. “There will be activities taking place in London that will only be able to take place on the territory of the European Union,” he said.

The leaders’ statements reflect an increasing feeling in European capitals that the hard line the prime minister and others adopted during the Conservative conference – including the home secretary, Amber Rudd’s plans to prevent migrants “taking jobs British people could do” – may reveal a far deeper hostility to the EU than they had imagined.

Despite well-publicised divisions, the EU 27 have shown consistent unity on Brexit. Charles Grant of the Centre for European Reform thinktank said in a research paper last week that this was partly because of a rising fear of Eurosceptic populism.

“A lot of British politicians believe that the hard line of the 27 is merely an opening stance,” Grant said. “Rather more Britons assume that, in the end, Angela Merkel will look after the UK. But for Merkel, the interests of the EU come first. She believes that maintaining the institutional integrity of the EU, and the link between the four freedoms, is in Europe’s interest and therefore Germany’s.”

He said many British politicians were over-optimistic about the kind of deal they might achieve because they failed to understand the continental debate on migration. “They tend to assume that because the British dislike EU migration, other Europeans must think similarly,” he said.

“In most EU countries the big issue is inflows of people from outside, not inside the EU. In Germany, for example, mainstream politicians do not see intra-EU migration as a big problem. So the 27 are not going to allow the British to combine single-market membership with controls on EU migration.”