John Curtice speaking in Westminster on Monday, April 3. Adam Payne/Business Insider LONDON — The British public wants Prime Minister Theresa May to deliver the sort of Brexit deal that the European Union has shot down on multiple occasions, polling data shows.

Most voters support Britain's free trade arrangement with the EU but at the same time are keen for May to impose stricter controls on migrants coming from the 28-nation bloc once the country has completed its exit.

Polling expert John Curtice presented the data during a conference at the Queen Elizabeth II Conference Centre, Westminster on Monday morning.

"The public is consistent on this," Curtice said at the "Article 50: What Next?" event.

"Free trade is popular. Immigration control is popular. You can already begin to see that the supposed trade-off is simply not there in public opinion. Voters both want free trade and immigration control. Therefore, we are talking about a fundamental difference between the principles by which the EU operates.

"It's not just a case of Britain wanting to have its cake and eat it. It's much more fundamental than that. The British public disagrees with the recipe by which the cake is baked."

40% of Brits reject the notion that UK government faces a choice between maintaining its current free trade arrangement with the EU and imposing tighter controls on EU migrants.

This is despite repeated warnings from EU figures like EU Parliament head Guy Verhofstadt and European Commission President Jean-Claude Juncker that Britain will not be allowed to unpick the Union's "four freedoms" as part of its exit deal.

The four freedoms require member states to accept the free, unlimited movement of goods, capital, services, and people. The free movement of people was arguably the biggest concern for voters in the June referendum.

Curtice's presentation also revealed that the public is split down the middle on whether it expects May to come away from Brussels with a satisfactory deal. Around 37% expect a good deal, while 32% anticipate a bad one.

May officially got the Brexit process underway last week when she triggered Article 50 of the Lisbon Treaty.

In a draft letter published last week, EU Commission President Donald Tusk stated that the Union wants issues regarding Britain's divorce, like the size of the divorce bill and residence rights of EU citizens, to be dealt with before talks can begin over a new free trade arrangement.