People often ask me, “Do you miss being an MP?” My answer is always a bit of a curate’s egg. I certainly miss being in government – where you can make change happen. But I don’t miss Westminster – even before the latest depressing revelations – it often felt to me like Hogwarts gone wrong.

But what I miss most of all is working in the constituency. For almost two decades my weekly routine involved hours of meetings with whoever wanted to talk to their local MP. In community halls and supermarket cafeterias I would listen, learn, and do what I could to help. Their stories, over the years, shaped my sense of the world. In that community, where I’d grown up, it was natural and normal for me to meet people from a wide range of backgrounds. It was a real gift.

MPs are often dismissed as “out of touch” but over the last couple of years – in “the real world” – I’ve seen just how many people live, work and socialise in ways that mean they rarely encounter people who are not like them. Think of all the remain supporters after the referendum expressing incredulity at the result, and then confessing: “But I’ve never met anyone who voted to leave.” Or the council leader after the Grenfell fire who admitted she’d never been inside a council tower block flat. When did living parallel lives, rarely really engaging with people who aren’t like us, become the norm for so many of us?

Of course there has always been difference, and indeed division, in our country. But the sense – that so many of us feel – that despite being more connected than ever we are living among strangers, has grown in recent years. Over these past months I’ve travelled the length and breadth of the country to make a programme for BBC Radio 4, exploring how we came to be so divided and what we can do – as a society and as individuals – to bridge those divisions.

The two places where people meet [in Oxford] are in the maternity ward … and in the mortuary Human geographer Danny Dorling

I started my journey in Oxford, home town of human geographer Danny Dorling, who explained that the wealth gap was pulling his community apart: “The two places where people meet are in the maternity ward … and in the mortuary – those are the two most socially mixed places in Oxford … It’s a fantasy to think that we can pay each other vastly different amounts of money and will actually understand each other and work well together.”

I’ve always believed that if we’re to come together as a country we need to close that economic gap through political action. But in a country where economics, politics and technology are pulling us apart, we need interactions that bring us together, where we can establish trust and understanding across difference.

Being a parent is for me a daily reminder that our relationships and connectedness are actually the heartbeat of our deepest sense of meaning and wellbeing. And in that insight, I’ve found myself in pretty good company: Pope Francis has long argued that alongside economic change, for human beings to flourish, we need to create a “culture of encounter”.

How would we create such encounters and what would they ask of us? The evolutionary psychologist Robin Dunbar described to me how over millennia, human beings had developed particular habits and rituals that had been proved to speed up bonding between people who didn’t have much in common. At the top of this list are singing, dancing and eating together.

So in a hall in South Norwood I met 30 senior citizens and 30 young professionals who’d gathered for a cèilidh organised by South London Cares. It’s an organisation responding to the fact that people over 75 are statistically the loneliest age group in the UK, followed by people aged between 21 and 25. And at the Goodtrees neighbourhood centre in Edinburgh I attended the community cook club that teaches people to cook, using surplus food donated by supermarkets to create shared meals.

As Ewan Aitken, chief executive of Cyrenians, the charity that’s now rolling out these clubs across Scotland, told me: “Food is only the catalyst to gather. The power lies in the relationships that are created around it and the fact you meet people you wouldn’t meet otherwise.”

The conversations on my travels certainly confirm how fundamental the economic gap is in our country today. But I’ve learned that as well as changing the system, maybe we need to change ourselves. Only by coming to know and coming to understand people who aren’t like us – by contributing to a culture of encounter – can we hope to also close the empathy gap that today divides us. And that’s a task not just for politicians, but for every one of us.

• A Culture of Encounter is on BBC Radio 4 at 9am on 14 November, or online at bbc.co.uk/radio4.

• Douglas Alexander is a senior fellow at Harvard Kennedy School, a former UK government minister and former shadow foreign secretary