Nearly half the public believes MPs should not be given a vote on the final Brexit deal, according to polling.
Some 53% want voters to have a say at the ballot box on the package but 47% were against the Commons deciding whether to reject or accept it, the BritainThinks research found.
Around one third believed MPs should be allowed to vote on the deal.
Less than a quarter of adults think the Government has done a good job so far in exit talks with the European Union and 56% said Labour's policy was not clear.
The poll also found that 64% believe it is likely the UK and EU will fail to reach an agreement.
BritainThinks released the polling as part of a wider report on Brexit that included research with two panels of eight people.
In the smaller research groups, swing voters believed Brexit would be a success and compared it to David Beckham because it is "going to get better with age".
Many had disengaged with the process and "very few" felt they had heard anything about the issue recently.
Floating voters were far more concerned with why the UK has not left the EU yet than how the negotiations are going, according to the report.
They compared Brexit to a unicorn "because it doesn't exist" and said it was "slow like a sloth", the strategy consultancy found.
- The national poll of 2,078 people was carried out between June 8-10.