Frances O’Grady, the TUC’s general secretary, has delivered a stark warning that Britain’s politicians risk fuelling the far right by failing to tackle the root causes of the anger that helped to drive the Brexit vote.

Speaking to the Guardian as union members prepare to gather for their annual congress in Manchester this weekend, with Brexit high on the agenda, O’Grady said more than two years on from the referendum, politicians had not done enough to understand the concerns of leave voters.

“I’m very clear that we need to look at the root causes of people’s anger, and often at the bottom of anger we find fear – and I think there are a lot of people in Britain today who’ve had a rough time for 10 years – no real pay increases; living standards not just stagnant, down. That’s not a recipe for peace and harmony, is it?”

She pointed to precarious employment, low wages, boarded-up high streets and cuts to schools and hospitals, as causes for the wave of frustration with the status quo that culminated in the referendum result.

“There’s been the slightly patronising language about people being ‘left behind’ – whoops-a-daisy you missed the bus,” she said.

“Whereas in fact, as far as I’m concerned, we’ve had a set of policies that have actively made life worse – at work, and in communities that feel abandoned, that feel neglected and ignored. And they’re right to, because schools have been starved of funding, hospitals are under pressure, and a lot of the jobs on offer are bad jobs – so people are right to feel angry.”

And with hate crime rising, and increasingly divisive rhetoric colouring political debate on both sides of the Atlantic, she warned that leaders must avoid creating conditions in which far right populism can thrive.

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“There’s a risk of it sounding pious but I think this is about the health of democracy, and democracy is under pressure,” she said. “There are material roots to this that need to be tackled, because if people don’t have the hope of a decent life, that’s when the far right does well.”

“There’s a danger of complacency about democracy,” she added. “Voting once every five years isn’t the beginning and end of it; it’s about whether people feel they have a voice; and whether they feel politicians are paying attention to them. Who’s minding the shop? What is happening in parliament, other than Brexit? If a community feels neglected, how much more neglected do they feel now?”

Many at Westminster interpreted the Brexit vote straightforwardly as a demand for tighter immigration controls; but O’Grady, who represented the remain camp in the televised Wembley debate during the 2016 campaign, alongside Sadiq Khan and Ruth Davidson, rejects that analysis as too simplistic.

“I’m always wary of politicians that want to tackle the symptoms rather than the cause,” she said. “Of course there were worries expressed about migration, of course that was a big issue during the campaign. But I also believe most people are decent, and that most people don’t believe low wages are the fault of other workers, wherever they come from. It’s the fault of the boss who’s exploiting them.”

Instead of choking off the supply of EU workers, the TUC is demanding that the government increase the national minimum wage to £10 an hour, encourage the return of collective bargaining to give workers the power to fight for better terms and conditions themselves and improve rights at work.

TUC analysis, based on official figures, shows that since Theresa May moved into Downing Street, promising to help the “just about managing”, the average household’s outgoings have outstripped income in every single quarter – by a total of £1,250. “What’s happened to her promise? Families on the edge need more than empty words,” she said.

“What we could do is get back to the TUC’s original demand that everybody should get a fair day’s pay for a fair day’s work – whoever they are, wherever they come from,” she said.

She fears many of the workers she represents will find their lives made even harder by Brexit. O’Grady has argued strongly for a close continuing relationship with the EU, helping to influence the gradual shift in the Labour leadership’s position, towards customs union membership and accepting key aspects of the single market.

“What we hear from business, from big companies like Jaguar, is if Britain leaves the single market and customs union, then don’t count on them for the future – and that’s big jobs,” she said. “The government’s own leaked advice shows that there’s a big price to pay; the question is how big?”

Several Labour-supporting unions have openly backed a second referendum on the final deal, and supporters of a “People’s Vote” are hoping the TUC will play an important role in framing the discussion at party conference later this month.

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But speaking before the TUC’s executive meets to discuss the issue, O’Grady sticks carefully to her long-held position: that the public should have a say, but a general election would the best way forward.

“My preference, I’ve always been clear about this, is a general election. I think there are problems about very complex issues being decided on yes/no ballots.”

As the negotiations approach their endgame, and with the Conservative party deeply riven over the right way forward, she is clear the Labour leadership may need to be flexible.

“Labour’s right to say keep all options on the table. That’s what we’ve been advising. Don’t make the mistake Theresa May has made, and box yourself into a corner, or tie yourself into red lines.”