The Survation survey claims 54% of Britons (54%) would vote to remain in the European Union if another referendum was held, while 46% would vote to leave.
It also showed a majority of 55% wanting a cross-party coalition of parties negotiating Brexit, compared to 32% still believing the Tory minority Government should do it alone.
A majority of 36% said the best outcome would be to stop exit talks altogether and work to stay in the EU, while 32% backed paying a fee for access to the tariff-free customs union.
According to the poll, only 24% of Britons support the Government’s current strategy of leaving the customs union in order to strike free trade deals with other countries.
However, 47% of Britons oppose a referendum on the final deal, while 46% think they deserve the right to vote on it.
Meanwhile, the poll shows the Tories at 41%, who have regained a one-point lead over Labour, down four points on 40%.
But a separate Opinium survey for the Observer showed Labour on 45%, six points ahead of the Tories on 39%.
That poll also showed Mrs May with a net approval rating of -20% following her disastrous general election, with Mr Corbyn on +4%.
Survation interviewed 1,017 British adults by telephone between June 28 and 30.