You may think it’s a commitment to buying a round, the ability to chat at length about the weather, or making a proper cup of tea. But when it comes down to what makes people proud to be British, there is a consensus across all ages, demographics and political groups – and tea, pints and the weather don’t get a look-in.

Hard work, fair play and community are the values that voters – no matter which political party, age group, social class or region they come from – instinctively believe capture what it means to be British, according to a large-scale study of British values by Public First.

“When you talk to people across Britain it’s clear they have a shared set of values – if fairness is Britain’s moral compass, hard work is its character and community the thing that binds us,” said Olivia Walsham, the director of social policy at the policy and polling research firm.

But the research found that while most voters could agree on this core set of values, they were deeply pessimistic about finding common ground: more than 65% of respondents felt that in a post Brexit-era, Britain is more divided than ever.

As Andy Burnham embarks on a summer “listening” tour of the UK and vows to “bring back hope”, the report suggests he has his work cut out, with fewer than one in three people feeling hopeful about the UK’s future, and seven in 10 feeling that things have become worse in the last five years.

But three-quarters of the public believed British people shared a common set of values – ranging from 70% of Reform UK voters to 83% of Labour-leaning voters.

In the study, which polled 6,000 adults and spoke to 300 people in focus groups, participants were asked to choose which values they thought were the most important – forcing them to make trade-offs.

“Hard-working” topped the list of qualities the public associated with British people, with 70% describing hard work as a British value. “Community” was also key, with 80% of people agreeing Britain was at its best when neighbours looked out for one another. Contributing to society boosted positive views: 62% of those who had volunteered in the last month said they were optimistic about their local area’s future, compared with 25% of those who had never volunteered.

Unsurprisingly for a population that can’t pass a queue without joining it, the notion of “fairness” or waiting one’s turn was the clearest shared value. Asked for examples of what described British life at its best, citizens referenced queueing, the NHS, fair play, taking turns, treating people equally, and the expectation that everyone should play by the rules.

The report also exposes deep-seated division, especially on immigration. Half of respondents said immigration had had a negative impact on the UK, while only one-fifth said a diversity of people and cultures made them proud to live in the UK.

Sunder Katwala, the director of British Future, said the report showed that British people had become not only more divided, but more “discomfited by how divided we feel”.

In a political landscape in which no political party was polling at higher than 25%, politicians were more likely to appeal to their base using divisive language, he added.

“Politics should be about articulating how people feel about the world, but also the peaceful resolution of differences,” Katwala said. “There are some glimmers of hope in this research, people are looking for a unifying sense of what we share, but actually appealing across the board to those people, it’s quite challenging.”

Burnham’s advisers may take heart in the report’s findings that messaging around shared values had been better received when framed positively, rather than through grievances, with “messages that talked about British values in affirmative terms consistently outperforming those that were rooted in a sense of loss”, according to the report.

“The values that unite us haven’t disappeared but no one is speaking to them,” said Walsham. “Politicians should start by recognising people’s everyday values – fairness, hard work and community. Then they might fan the flames of a hopeful, shared patriotism that the country so desperately needs.”

Trevor Pears, the chair of the Pears Foundation, which funded the report, said people were crying out for more initiatives like the annual Big Lunch and Big Help Out projects. “We need many more opportunities for people to come together, help one another and strengthen the communities they’re part of,” he said.