This is a story of hope and optimism. During the last European parliamentary session in Brussels, I sat down with a fellow British MEP over a coffee to discuss how we might work together to encourage a peaceful solution to the crisis in the straits of Hormuz near Iran.

We had each been contacted by the Foreign Office because of our membership of the European parliament’s delegation on relations with Iran. It’s not a particularly influential body, but it does have a voice. However, what gave me hope was not the delegation, but the fact that my colleague in question was a Liberal Democrat. We may have diametrically opposing views on Brexit, but here we were striving to solve an equally intractable problem.

While the two major parties are engaged in the war over our membership of the EU, neither is in good shape to win the peace that follows

Brexit has shattered the British postwar consensus, polarised political parties and weaponised our national conversation. Pretty much every relationship in our lives is now subject to the gravitational pull of either leave or remain. I fell into the Brexit vortex three months ago, frustrated by my perception of MPs’ betrayal of the 2016 referendum, and was spat out as a Brexit party MEP. Since then I’ve been happy to hold the EU, government and official opposition to account. It’s cost my family some life-long friends, one of whom says they are “never going to speak to that man ever again”. Many of my former work colleagues in the third sector, instinctively of the remain persuasion, can’t quite get their heads around it.

I’m not looking for sympathy. My concern is what happens to our national psyche when it’s all over. When we’ve left or remained. Will it be like the morning after a particularly wild night before, when we all feign amnesia and pretend nothing happened? Or will the recriminations and bad blood continue to fester?

Neither of our two major political parties have thought much beyond the immediate crisis. Both are reacting in fear of the Brexit party and Lib Dems. They are right to be scared: the Brecon and Radnorshire byelection saw Labour relegated to fourth place and the Tories losing thanks to the Brexit party. But if either think there’s any chance of Britain returning to a cosy two-party duopoly, they’re kidding themselves.

Whether we leave or remain, post-Brexit Britain is going to look and feel very different to where we are now. While the two major parties are engaged in the war over our membership of the EU, neither is in good shape to win the peace that follows. Brexit is about much more than our relationship with the EU, it’s about how we govern ourselves in the future.

For all the talk of one nation Conservatism and national unity, Boris Johnson’s one-dimensional government is locked and loaded on saving its own skin. “Do or die” is the only strategy open to a government that has spent three years negotiating against itself. That may be what’s needed to lance the Brexit boil, but it’s not a formula to engage the 48% who voted to remain, including many existing and potential supporters.

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The same issue lies at the root of Jeremy Corbyn’s problems. In moving towards a remain agenda, he is turning his back on 17.4 million leave voters, including huge numbers of Labour supporters.

With a possible general election in view, both parties have been busy promising voters lots of new goodies to try to secure their support. But this is not enough to heal the toxic Brexit divide, to reunite families, colleagues, communities and the union.

I’m not a fan of proportional representation, but our first-past-the-post system leaves many voters unrepresented. Our second chamber, the House of Lords, is way past its use-by date. The yah-boo politics of the Commons may be entertaining, but it’s no way to run a 21st-century democracy. The command-and-control relationship between Whitehall, devolved administrations, local government and civil society needs to be rebalanced.

Despite profound differences, the irony is that the two challenger parties – the Brexit party and the Lib Dems – share a common aim in challenging our self-serving two-party system. I believe that we could both force the issue once more, this time to reboot our politics, bring the nation back together and rebuild trust in our democracy. Call me optimistic, but perhaps a coffee would be a good place to start.

• Matthew Patten is the Brexit party MEP for the East Midlands