Only 7% of the public believe the government has handled the Brexit negotiations well, according to research.

Frustration is shared across the referendum divide, with 80% of leave voters and 85% of remain voters believing ministers are not doing a good job of overseeing Britain’s departure from the EU.

Just 6% of people expect Britain to get a good deal from the negotiations. John Curtice, the influential psephologist who analysed the survey data from the National Centre for Social Research (NatCen), said it was striking how leave voters had become just as critical as remain supporters of both the Brexit process and the outcome.

The findings are based on the views of more than 2,600 adults who were interviewed last month about their views on Brexit. When the results were compared with data from 2017 it was found that public faith in the negotiations has fallen dramatically.

Out of those interviewed in 2017, 41% said the talks were being handled badly by the government, and 29% thought ministers were doing well.

The research also found both leavers and remainers were as likely to think the prime minister’s deal is a bad one – 66% and 64% respectively – up from 20% and 56% in 2017.

The research suggested a rise in the number of people who think Brexit will have a negative impact on the economy – up from 46% in 2017 to 58% in 2019. The rise in economic pessimism has occurred primarily among those who voted leave.

“Given the polarisation of attitudes, there was always a risk that the Brexit negotiations would result in an outcome that would fail to satisfy most voters,” said Curtice, senior research fellow at NatCen and chief commentator at What UK Thinks.

“But what, perhaps, is particularly remarkable is that leave voters have become just as critical as remain supporters of both the process and the outcome. That is not an outcome that would necessarily have been anticipated, and certainly does not help the prime minister in her efforts to secure parliamentary approval of the deal”.

There has been little change in perceptions of Brexit’s impact on levels of immigration to Britain. Nine per cent of those polled think immigration will be higher after Brexit (compared with 7% in 2017) while 39% think it will be lower (43% in 2017).

However, exactly half of those surveyed do not believe Brexit will affect immigration levels at all (48% in 2017).

In terms of the hypothetical outcome of a second referendum, the research found that 55% would have voted to remain had a new vote been held in February this year.

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Curtice wrote: “It is enough to raise doubts about whether, two and half years after the original ballot, leaving the EU necessarily continues to represent the view of a majority of the British public, but given the potential frailties of all survey work the remain lead in our data is not sufficiently large for anyone to be sure what the outcome of any second ballot would be, especially as any such ballot would occur after a campaign that might result in a shift of opinion in one direction or the other.”

One of the most significant sources of the apparent swing to remain since 2016 is from voters who did not participate in the referendum but have become more inclined to vote remain as the process has unfolded.

There were initial signs of this shift months after the referendum, when 43% of those who said they did not vote in 2016 stated they would vote remain, compared with 32% who indicated they would vote leave. However, this gap has gradually widened to the extent that 56% indicate they would vote remain while just 19% state they would back leave.

“Inevitably, there must be a question mark about whether those who did not vote first time around would necessarily do so second time around,” wrote Curtice.

The report concluded that there is reason to believe that a second ballot might potentially produce a different outcome, although it is far from certain that it would do so.

“Perhaps the key message for the politicians as they decide what to do about the next stage of the Brexit process is that, having been widely seen to have done a poor job of implementing Brexit so far, those on all sides of the argument might be best advised to show a degree of humility when claiming to know what voters really want,” wrote Curtis.