Free trade, roaming limits, and airline compensation remain some of the popular EU rules in the UK
A new report has shown that 88% of British voters want to maintain free trade with the EU after Brexit - but 68% want an end to freedom of movement.
The report from NatCen look at the public's expectations of the UK government's eventual Brexit deal.
Negotiations between Britain and the EU will get underway once Theresa May triggers Article 50 of the Lisbon Treaty on March 29th.
In a survey of 2,322 people, the study found that 82% of Leave voters and 58% of Remain voters want potential EU migrants to Britain to be treated in the same way as migrants from outside the EU.
However, an even greater percentage of voters - 86% (Leave) and 54% (Remain) - believe potential migrants from Britain to the EU should be treated the same as those arriving from outside the union.
There is overwhelming support for the maintenance of free trade from voters on both sides: 88% of Leave voters and 91% of Remain supporters.
Significant majorities on both sides also support maintaining a number of EU benefits and initiatives - such as mobile roaming cost limits, minimum standards for water quality at beaches, and rules on compensating passengers who have experienced delays.
Professor John Curtice - the report's author and a senior research fellow at NatCen - said: “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."
Professor Curtice added: “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."