As Commons Leader Andrea Leadsom signalled a more consultative approach, the Survation survey also showed just over half want a cross-party coalition of parties to negotiate the UK's exit from the EU, compared to less than a third who think it should fall to the Tory minority Government alone.
Theresa May found herself ahead of Jeremy Corbyn on which leader voters trust more to negotiate the best deal, at 51 per cent to 35 per cent respectively.
However, a majority said the best outcome would be to stop exit talks altogether and work to stay in the EU, while around a third backed paying a fee for access to the tariff-free customs union.
Less than a quarter support the Government's current strategy of leaving the customs union in order to strike free trade deals with other countries, as Labour signalled its strongest backing for staying in the bloc yet.
However more Britons (47 per cent) oppose a referendum on the final deal than support it (46 per cent).
Meanwhile, the poll showed the Tories regaining a one-point lead over Labour.
But a separate Opinium survey for the Observer showed Labour on 45 per cent, six points ahead of the Tories on 39 per cent.
That poll also showed Mrs May with a net approval rating of -20 following her disastrous general election, with Mr Corbyn on +4.
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