“The polls called the referendum wrong” is a common misapprehension. In fact, while they were clearly wrong in the past two general elections, opinion polls were mostly right – at least within a margin of error – all the way through the 2016 referendum campaign. Although most commentators chose to interpret the polls through the prism of their own confirmation bias (what their friends thought would happen), and therefore assumed remain would walk it, the eventual close-run win for leave was fairly well predicted.

Latest polling suggests that remain has improved its showing a little – although the net result is still “neck and neck”, too close to call. The problem with most polls, however, is not that they might be wrong but that they mask how polarised British voters’ views have become.

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Our work at BritainThinks identifies four Brexit tribes, not two, and shows that as much as two-thirds of opinion is clustered at the extremes. We identify the “diehards” who were delighted by the original referendum result, and have few significant concerns about leaving the European Union. At the opposite end of the spectrum sit the “devastated pessimists”, who were extremely disappointed by the result and can see no positives at all in leaving.

These two groups represent more than 65% of the public, while the remaining third is made up of two groups: cautious optimists and accepting pragmatists – the former being broadly in favour of leaving but voicing some concerns, while the latter is disappointed overall but can also see some upsides to leaving. Polls focusing on a binary choice flatten out these important nuances and ignore the crucial swing voters in the middle.

They also disguise how fragmented Britain has become. I asked voters last week to describe the UK in three words. They chose a variety of pretty negative descriptions: “struggling”, “fearful”, “uncertain”, and “pessimistic” came up again and again, but the word that was chosen almost unanimously was “divided”. Seven out of 10 of us of us believe Britain will become still more divided in the coming year. These divisions cut through age, gender, geography, class and education. They also speak to a deep sense of inequality: 64% describe themselves as “have-nots”. Focus group members in small towns all around the UK spontaneously describe their area as a “left-behind community”.

Brexit has highlighted deep-rooted inequalities and values differences that have existed for many years

However, voters are united in their view that Brexit is not going well – although this is driven more by impatience (“why hasn’t it happened already?”) than detailed analysis of the negotiations. Playing the focus‑group game of “If Brexit were an animal, what would it be?”, voters say it is the slowest animal they can think of: a sloth or a tortoise. They are also united – and doubly frustrated – that the Brexit process is distracting politicians from the issues that really matter, and feel far more tangible: the high cost of living, precarious employment, housing shortages, rising crime and, most of all, cuts, especially cuts to the NHS. Some worry out loud that “dragging out” the negotiations is an excuse to insure against these failures.

Among the public, there is some anxiety about the prospect of “no deal” but little clarity about what it would mean. Most expect that the current deal (which they struggle to describe) will be rejected by parliament, and are even more concerned about what they assume will be more political turmoil, and continued stasis on the policy areas they regard as priority. They feel that they, the public, have been left out of the discussion, and this may explain a growing public appetite for a further referendum – although there is considerable concern about what the terms of the vote might be.

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Against the backdrop of division, Brexit must be seen as a symptom not a cause. It has highlighted deep-rooted inequalities and differences in values that have existed for many years, and for this reason many “diehard” leave voters still believe that the long-term gains of leaving the EU will be worth any short-term pain. Although, as the prime minister has noticed, eight out of 10 say they want to see “the country come together”, it is hard to see how that can happen – wherever the Brexit negotiations and any subsequent votes take us – until those issues are addressed.

• Deborah Mattinson is founder director of the research and strategy consultancy BritainThinks