All told, it’s not been a good few months for the standing of our politicians. Whether you think there was a good case to have a referendum on the UK’s membership of the EU or not, the reason we were all put through it was ultimately one of internal Conservative party management. A fundamental question about who we are as a nation and how to best represent our interests was embarked upon because David Cameron thought it was his best way to silence his critics on the Tory right and prevent defections to Ukip. Indeed, Labour strategists long saw a referendum as an opportunity to exacerbate the split that has riven the Conservative party for decades and keep them “banging on about Europe”.

In the end, the referendum campaign itself became a story of “blue on blue” attacks, and old scores forged long ago on the playing fields of Eton being settled. Naked political ambition and (mis)calculation seemed to define who sided with which team; Boris Johnson was memorably described by The Economist’s Jeremy Cliffe as “making arguments he knows are wrong for a cause in which he does not believe to win a job for which he is wholly unsuited”. And then of course, when the going got tough, everyone resigned.

All of which can only have heightened what Fabian Society public attitudes work a few years back found to be one of the main reasons people have lost trust in politics: they feel “politics is a game played by an out of touch elite who live on another planet”. This idea of politics as a game was identified by the academic and former Labour MP Tony Wright as being particularly important because it allows “questions not to be answered, truths not to be told, facts to be distorted, complexities ignored and political opponents traduced, all in pursuit of political advantage”.

This feels like a fairly succinct summary of the referendum campaign. But if that provided a showcase for many of the worst aspects of our political culture, perhaps even more concerning is what happens next. While we’ve been told by the new PM that “Brexit means Brexit”, it’s quite likely that Brexit won’t ultimately resemble what many leavers thought they were voting for. Matthew Taylor related on his RSA blog how the Friday after the referendum “an angry woman from Hartlepool rang the BBC; ‘we voted out but I’ve turned up at my hospital and there’s no sign of any extra money’.” This is an extreme example, but at the very least the referendum signalled a desire for greater control over immigration, something that it’s unclear whether our politicians will be willing or able to deliver, given the likely economic consequences.

So the big question now is whether politics is capable of bringing us together rather than driving us even further apart. These are febrile and worrying times, fertile ground for demagogues and populists – as Donald Trump’s improving poll numbers across the Atlantic show. To counter this, we need two things.

First, we need inspiring, hopeful and generous political leadership, that builds common cause and shapes the national conversation in an open, tolerant and optimistic direction. It is important that politicians have plans, as the failure of the leave campaign to “take control” after Brexit, and recent criticism of Jeremy Corbyn’s inability to make progress on policy, have shown. But, as I have argued elsewhere, Labour politicians have tended to put too much weight on policy as the be all and end all of their role, and conflate proposals for legislation with leadership. Instead Labour’s Westminster politicians need to do fewer, bigger things: establish in the clearest possible terms the party’s purpose and define the parameters of its political offer – and then seek to inspire collective action.

Second, we need to build a new politics from the bottom-up. Brexit was in many ways a revolt against our professionalised politics, how remote it has become from people’s lives and how little control we are allowed to feel over the things we value most: the work we do, the places we live, and the people we share our lives with. The EU, as the most distant and bureaucratic political institution of them all, perhaps understandably felt the force of this dislocation when people were asked the question. The way to counter this is not to ask the question again and hope to get a different answer, nor to try and turn the “48 per cent” into the “51 per cent”. Instead, we need to make sure politics starts where people live. The Fabian report Pride of Place argued that people need to feel empowered to make changes to improve their own neighbourhoods before we can reasonably expect them to feel they can change the world. This was primarily an argument about climate change: if you don’t feel like you can stop people leaving litter on your doorstep, or you’re scared to go in your local park because it’s become an anti-social space, how could you possibly think you might prevent the seas rising?

The same is true of our politics – we need to build a sense that politics is about the conversations we have in our communities, that turn into action to change the neighbourhoods we care about. This is the way we build the strong sense of social solidarity and community spirit that an open and outward-looking social democracy requires. A new politics means spreading democracy not just through our political system so power is meaningful at the lowest possible level, but through all spheres of life: through the economy and through our public services. We need more than ever, as GDH Cole wrote, “to enlist the active participation of as many as possible … in the task of democratic self-government”.

Ed Wallis is editorial director and senior research fellow at the Fabian Society.