I told about five people that I was going to something called a death cafe – the reactions were mixed, but none was particularly positive. "Will it be full of goths?", "How morbid", "That's weird." The thing is that people don't just find talking about death uncomfortable – they find the idea of talking about death uncomfortable. In general, we just don't do it.

This is what inspired Jon Underwood to create the non-profit death cafe in 2011, based on the Swiss Cafe Mortel movement. As he saw it, western society has long outsourced discussions about death to doctors, nurses, priests and undertakers. The result, says Jon, is that we have lost control of one of the most significant events we ever have to face.

He suggested to various cafes in east London his idea of setting up a place to go and talk about death, but there were no takers. So the first death cafe in the UK was in Jon's own house in Hackney and was run by his mother, Sue Barsky Reid, a psychotherapist.

It was a great success and interest grew, leading to the events, which are usually about an hour long, popping up in a range of venues from cafes and private houses to a cemetery and a yurt. The premise was simple: people go along, drink tea, eat cake and discuss death: not to be morbid, just to raise awareness and to "help people make the most of their (finite) lives".

Jon and Sue went on to produce a guide to running your own death cafe, which was published in 2012. Since then, hundreds of people have been hosting them around the world.

I went along to an event in central Edinburgh at a bohemian cake shop called Lovecrumbs. I had no idea what to expect, so I met with one of the organisers beforehand, Katherine Newbigging, director of Just Festival, who brought along Rebecca Paterson, who works for Good Life Good Death Good Grief, a campaign that has been involved in hosting other death cafes in Scotland.

Katherine Newbigging greets visitors to the death cafe in Edinburgh. Photograph: Murdo Macleod for the Guardian

I wanted to find out what brought people to the gatherings, which were undoubtedly popular: Katherine told me that the Lovecrumbs event that evening had a reserve list of guests as they were expecting to be full. "People are just interested. It's something a bit different. There aren't many places where talking about death is OK. We want to provide that environment, and help lead the discussion."

Rebecca agrees. "Talking about it can only be a good thing: not only does coming to terms with your own mortality mean you're more likely to live life to the full, being open about it means we can support each other, our families and ourselves when death has an impact on our lives. It makes for a healthier, happier community."

She paused, and for a second looks moved: "I've heard of people saying that death can be a really special time. Imagine that – how differently we would all feel about it if that could be the case?"

This struck a chord with me. My sister is a doctor who works in palliative care, and she has told me about talking to the families of frail, elderly patients with multiple illnesses. She tells family members that their loved one is going to die – they simply can't believe it and aren't equipped to deal with it, or even support the person involved. How have we got to the stage in our sanitised society where we can't bring ourselves to believe anyone is going to die?

It made me think that less than 100 years ago, death would have been all around us. People had big families because it was expected that some would die in infancy. Men went to war and never came back. Women died in childbirth. And not many people made it past middle age. Compare that with now: we all live so much longer, our lives sometimes prolonged by advances in medical care. The result is that we can now reach 35 or even 40 without ever having a relative die. Through what Underwood refers to as the "outsourcing of death", and through this lack of exposure to it, we have become ill-equipped to deal with it – and in denial of the one thing that affects us all.

At 6pm, Katherine hushes the assembled tea drinkers in Lovecrumbs and announces the start of the meeting. Customers who didn't know about the death cafe gulp back their tea and leave hastily, staring at us in concern and fascination. Menus are passed around: a list of questions for discussion, divided into starters, mains and tea & coffee. The questions, Katherine reassures us, are just conversation starters, and not to be stuck to rigidly. Between each course we will move around, to make sure everyone speaks to someone different.

I sit down next to a woman in her late 50s, Lesley. We scan the questions on our starters list: "Cremation or burial?", "Nature taking its course or assisted suicide?", "Where would you like to be when you die?"

For a second I feel daunted – these are certainly ice-breakers. But somehow, talking to someone you don't know about such things is a lot easier than starting a conversation about churchyards versus woodland burial with your husband when he gets in from work.

Lesley and I chat about the questions briefly before moving on to why she is here: "I suppose I'm interested in how people who want to talk about it actually do talk about it. Is death taboo? I'm not sure it is. But sometimes I think that talking about dependency – being dependent on others as you reach the end of life – is taboo. It worries me that so many people these days have a problem with that. As a child, you're dependent, then you're independent, then you become dependent again. That's what happens. It's nothing to be ashamed of. If we talked more about the inevitable, at least it would be easier to plan."

The woman next to her nods enthusiastically at Lesley's words.

S o I leave them to finish their starters and sit down with Rae and Rachel, two young women, both with fresh grief etched on their faces, and looking slightly daunted. Death cafes don't offer bereavement support or counselling, but sometimes it could be that people who have experienced death suddenly feel the need to talk about it. That is why Rae and Rachel have come. "We've lost someone close to us, unexpectedly," Rae explains. "We're not here to talk about that though – we talk about it all the time anyway. It's more that, since it's happened, I've been more open. And I suppose it's OK to talk about dying in general to your friends, but to talk about me dying? They would think that was morbid."

When we get on to the mains, the questions are a bit lengthier – the ice-breaking is over, and it is time for some in-depth discussion, with starters-for-10 such as: "What things do you think make for a good death?" and "What words do you want on your tombstone?" The room is noisy with chatter at this point, to the extent that Katherine has trouble getting everyone's attention. There are no tears, serious voices or solemnity, just animated discussion.

Eventually Katherine bangs a teaspoon on a cup to tell us all it is time for the tea & coffee part of the menu, and we all swap tables again. There are only two questions: "What song would you like at your funeral?", and "How would you like to be remembered?". These positive themes are happily discussed at my table. I turn to the woman next to me, Rebecca, and asked what has brought her to the cafe. She tells me that she was a death doula, which fascinates me, as I've always felt that so much planning goes into the hugely significant event of giving birth, but very little into the event of dying.

"I have a background in nursing, which gives me essential expertise, but a death doula is not a nurse," she says. "It's a completely different approach, in that it's not allied to medicine or the medical 'narrative'. It's led by the individual themselves – the person who is dying. It's somewhat similar to the role of a birth doula."

For someone who works with death, surely the cafe was a busman's holiday? Not at all, says Rebecca. "I wanted to see where other people were at in the discussion of death – it's very much part of my job so it's a lot easier for me to discuss, but I can't assume everyone else feels that way. I also wanted to find out what people felt about having someone there, other than family – someone like me, a death doula. What did I get from my discussions tonight? I feel as though people are keen to personalise their deaths – and their lives. And I'm glad."

The cafe winds down to a natural end after its official hour, but many linger, deep in conversation. I hail a cab and the chatty driver asks what I've been up to this evening. I hesitate, then tell him. And that was it, we are off, talking about death, to the point where even after we reach my house, we sit in the taxi for 20 minutes chatting before I go in. It seems that people really do want to talk about death.

• deathcafe.com