More than a third of voters believe Britain may end up remaining in the European Union, according to polling.
Around one in five, 22%, said they did not know if the UK would follow through with its Brexit vote, while 16% are convinced the country will defy the result.
Nearly half the public, 48%, want a general election before negotiations begin, so voters can give their verdict on each party's plans for life outside the EU.
Some 59% of respondents were not confident the government will get the best deal for Britain, rising to 76% of Remain voters, according to the Ipsos Mori poll for BBC Newsnight.
It found that 5% of Leave voters would now change their vote compared with 2% of Remain voters.
A total of 42%, including 18% of Leave voters, said Britain should continue to allow EU citizens to live and work in Britain in return for access to the single market.
Some 38%, however, said losing access to the single market would be a price worth paying for new curbs on immigration.
Ipsos Mori interviewed 1,077 people on Wednesday and Thursday.
A separate poll for the Evening Standard showed similar results - with more than half of respondents (52%) backing a general election this year once the Tories have chosen a new leader.
The BMG Research survey of 1,016 UK adults also showed that the referendum result would be reversed if it were held today - with 45% backing Remain and 40% Leave - while 13% of Leave voters said they regretted their decision.