Britain has to keep unlimited immigration after Brexit if it wants a free-trade deal, senior European governments are demanding.

In a survey that shows how big the challenge will be for Theresa May’s government in negotiating a good Brexit deal, the governments of the 27 remaining European Union (EU) nations laid out a series of demands before Britain is allowed to leave.

Financial news organisation Bloomberg asked the various governments what they will put forward in the negotiations. Some of the most powerful nations, including Germany, said Britain must keep freedom of movement in return for access to the single market.

Even though many analysts see the lack of flexibility over migration rules as one of the key factors that made Britons vote for Brexit, there is little evidence EU states are willing to compromise. Only Denmark, Austria and Bulgaria said they shared Britain’s concerns about open borders.

Some demands, however, will likely be rejected outright, such as Spain’s desire for joint sovereignty over Gibraltar.

The demands suggest a tough job ahead for Prime Minister Theresa May and Brexit Minister David Davis, who will want to soften the positions being taken by other nations.

Mrs May said last month: “There was a very clear message from the British people in the Brexit vote that they did not want free movement to continue as it had done previously.”

Earlier this week, two former ministers warned the Prime Minister she would face a backlash from the electorate if she does not end freedom of movement.

Theresa Villiers, the former Northern Ireland Secretary, said the government must end “open door” immigration after the vote to leave the European Union (EU).

Former Work and Pensions Secretary Iain Duncan Smith added: “It is my view that we will have left the EU by the time of the next election which means we have to have a system in place that controls migration.

“People are living in cloud cuckoo land if they think the British voters did anything else but absolutely vote to take back control. It was very explicit that means migration and that’s exactly what they voted for.”