Voters disapprove of Theresa May’s handling of Brexit but the country remains deeply divided over the decision to leave, according to a new poll for the Observer.

The Brexit process is proving more complicated than some voters thought and more are now pessimistic about the process than optimistic. However, few back the idea of holding a second referendum that could see Britain stay in the European Union.

Half of voters (49%) disapprove of the way in which the prime minister is handing the Brexit process, according to the Opinium poll. Two in five Leave voters (39%) disapprove of her stewardship of the issue. Overall, only 27% approve of her handling.

While 34% are more pessimistic about Brexit than at the time of the referendum, 23% are more optimistic. Only 20% expect the UK to emerge with a satisfactory deal from Brexit talks, with twice the number (44%) believing that outcome to be unlikely. Most say the Brexit process is proving more difficult than they expected (51%).

Yet the poll suggests concerns have not translated into large numbers of people changing their minds over how they voted. In fact, there is support for leaving the EU with no deal. More voters opted for that outcome (37%) than the alternatives of entering a transition period where we remain in the EU single market until we can negotiate a satisfactory deal (25%), or abandoning Brexit altogether (23%).

While 40% of voters back staying in the single market “even if it means allowing free movement of labour”, some 37% want to end free movement “even if it means we leave the single market”. There was a huge split in polling between Remain and Leave voters, with 74% of Remainers prioritising the single market and 66% of Leavers believing that ending free movement was more important.

There is little appetite for a second referendum that would give a choice between the deal on offer and remaining in the EU. Most voters (53%) said that they did not want a second referendum, compared with 35% who did. Even a quarter of Remainers opted against another vote. Meanwhile, it appears pledging one would enrage those who voted Leave, with 82% against another national poll.

A second referendum is a virtual dead heat, with Remain on 46% and Leave on 45%. Only 5% who voted Remain last year and 6% who backed Leave appear to have changed their minds. The polling was conducted online among 1,005 people on 19 and 20 October.

Adam Drummond, from Opinium, said the public were giving May “little credit for her handling of it so far”.

“Nearly twice as many disapprove of the prime minister’s handling of the issue as approve, a slight decline on her position last month,” he said.

“Despite feeling that the process is difficult and being handled badly, few appear to be changing their underlying views. Indeed, 54% of Leave voters agreed that ‘Brexit is a good idea in theory but is being badly executed’.

“The country is still split down the middle on the issue with little sign of a decisive shift one way or another.”

Other polling experts believe the tide may be turning against Brexit among working-class voters. Peter Kellner, the veteran former YouGov pollster, said he believed there could be a “gradual shift” taking place among working-class (C2DE) voters.

“[In] polls since the start of August, we see a steady decline in the proportion of C2DE voters saying Brexit was the right decision,” he wrote in Prospect magazine. “This feels more like a change in working-class attitudes than a sampling fluke; though whether it is lasting or temporary remains to be seen.