A poll has revealed that nearly seven out of ten voters want tougher border controls for EU migrants
Data from the National Centre for Social Research showed that 68 per cent of adults quizzed would like to see newcomers from EU member subject to the same entry rules as those from non-EU nations.
Yet a massive 88 per cent of voters were also in favour of continuing free trade with EU member states, the poll showed.
The polling figures were being seen in Downing Street last night as an endorsement of Theresa May's aims of regaining control over Britain's borders from Brussels while also winning the best possible trade deal with the EU.
They come as the Prime Minister prepares to begin the Brexit negotiations with a request for the triggering of the EU's Article 50 exit mechanism next Wednesday.
Whitehall trade officials have begun examining international rules that could allow tariffs between Britain and the EU to be kept at zero for 10 years under one possible option.
Yet 88 per cent of voters were in favour of continuing free trade with EU member states
Support for free trade was down slightly from 90 per cent to 88 per cent while support for treating EU migrants like non-EU migrants was down from 74 per cent to 68 per cent.
A smooth and orderly process of exit will be in the interests of both sides
Support for continuing free trade with EU countries was firm across voters for all political parties, with 93 per cent backing from Tories and 84 per cent from Labour supporters.
Fewer Tory voters (44 per cent) were willing to concede free movement in order to maintain free trade, compared with 63 per cent of Labour supporters.
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Professor John Curtice, senior research fellow at NatCen and author of the report, said: "The stance taken by the UK Government of wanting to end freedom of movement but maintain free trade fits well with the views of most Conservative voters.
"But it also means that they are also the group that are most likely to be disappointed if they were to come to the conclusion that the Government has failed to achieve that objective.
"Theresa May could be faced with political difficulties at home if she struggles to achieve her key objectives in Brussels."
Figures in the report showed many voters of both the Leave and Remain campaigns at the EU referendum last summer now wanted similar outcomes from the Brexit negotiations.
Theresa May aims to regain control of Britain's borders from Brussels
A majority of Remain voters (58 per cent) wanted EU migrants to face the same border controls as non-EU migrants when coming to the UK, compared with 82 per cent of Leave voters.
Fifty-four per cent of Remain voters thought EU migrants should also face full customs checks on arrival in the UK and 51 per cent thought migrants should not be able to claim welfare benefits in the country.
Prof Curtice added: "For the most part, Remain and Leave voters are not at loggerheads on the kind of Brexit they would like to see.
"Many Remain voters would like to see an end to the less popular parts of Britain's current membership of the EU, while many Leave voters would like to retain the seemingly more desirable parts, such as free trade, cheap mobile phone calls, and clean beaches.
Voters' hopes for Brexit had changed little since a previous survey last November
"This is perhaps typical of the pick-and-mix attitude to the EU that has characterised much of Britain's relationship with the institution during its 44 years of membership so far."
Mrs May's suggestion that the UK should continue to pay Brussels to maintain access to certain EU programmes, as long as it does not involve large sums, was also backed by voters (55 per cent Leave, 67 per cent Remain).
More than half (54 per cent) of Leave voters think the UK should continue to participate in EU-wide university research programmes, a stance backed by 80 per cent of Remain voters.
On EU regulations, a majority (67 per cent Leave, 83 per cent Remain) want to keep standards for water quality at beaches, rules making British mobile phone companies limit the cost of calls while abroad (67 per cent Leave, 80 per cent Remain) and laws requiring UK airlines to compensate delayed passengers (64 per cent Leave, 77 per cent Remain).
:: NatCen interviewed 2,322 people between February 2 and March 5, either via the internet or over the phone.
Meanwhile, it emerged yesterday that officials in International Trade Secretary Liam Fox's department are looking closely at World Trade Organisation rules that allow tariffs between two trading partners to be kept at zero for a decade.
Agreement of both parties is understood to be required for such a transitional arrangement.
A Government spokeswoman said: "We are confident that this can be done in the period set out in Article 50, not least because unlike other trade negotiations the parties will be starting for a point of equivalence.
"A smooth and orderly process of exit will be in the interests of both sides, which is one of the reasons why we hav spoken about a phased process of implementation."