It found that an overwhelming majority want Britain to continue trading freely with the European Union – but also to end the automatic right of EU nationals to work in this country.
The survey by NatCen Social Research spells out what Britons would like to see emerge from forthcoming negotiations over Brexit.
1) Free trade
An overwhelming 90 per cent want the UK to still trade freely in goods and services with its European neighbours after quitting the EU.
2) Immigration controls
Seven out of 10 (70 per cent) think Britain should be able to limit the number of EU citizens coming to live and work in the country. That position is shared by 54 per cent of Remain voters. In addition, 74 per cent believe EU nationals should have to apply for permission to live in the UK in the same way as those from outside the bloc.
3) EU citizens already here can stay
A belief held by 86 per cent of Britons, including 68 per cent of Leave supporters.
4) Protect the City
Almost two thirds (63 per cent, including 57 per cent of Leave voters) said EU and British banks should be able to provide services to people within one another’s territories.
Wishlist five: Fishing rights Some 61 per cent, including half of Leave voters, said EU boats should be allowed to fish in UK waters in return for British boats retaining access to European waters.
5) Mobile phone charges
By a majority of well over two to one (46 per cent to 18 per cent) people believe Britain should continue to follow EU regulations on the cost of mobile phone calls abroad.
7) Customs checks
Seven in ten think customs checks should be introduced on people and goods coming from the EU.
8) No more NHS care
Nearly two-thirds (63 per cent) think EU citizens should lose their right to free NHS treatment.
9) Irish passport checks
The reintroduction of passport checks between the Republic of Ireland and Northern Ireland is supported by 45 per cent of people, against 29 per cent who took the opposite review.
10) Retain EU safety rules
The requirement for British firms to comply with EU safety rules were backed by 65 per cent. The split between the public’s preference for a “hard Brexit” or a “soft Brexit” was underlined when the public was asked to choose between maintaining free trade or reinstating border controls.
Voters opted by the narrowest of margins for immigration controls, with 49 per cent thinking freedom of movement for EU citizens should be kept if it enables the UK to keep free trade, and 51 per cent opposing it.
NatCen’s senior research fellow, Prof John Curtice, said: “Irrespective of how they voted, voters in Britain do not feel that the UK’s exit from the EU should necessarily be a choice between a ‘hard’ or a ‘soft’ withdrawal.
Rather, many back options on both menus. “Consequently, the kind of deal that is most likely to prove electorally popular is one that maintains free trade but permits at least some limits on EU migration.
“That, of course, is the deal that many in the EU insist will not be possible. In those circumstances, the UK Government will be faced with a tough choice.
“But given that most Leave voters – and, indeed, a majority of Conservative voters – prioritise limits on immigration over keeping free trade, perhaps we should not be