The woman sitting opposite me in an Edinburgh cafe is called Rebecca Green. She is in her early 40s, with a soft Birmingham accent and a gentle, smiling face. She is a nurse. But she also does something else – something that has prompted both fascination and animosity in those she has told about it. She is a death doula.

Birth doulas support women and their families through the process of a child being born. And death doulas support people during that other huge event – the one we don't like to talk about. The idea is hardly new, but in the western world, death has become a medical matter, says Hermione Elliott, director of the charity Living Well Dying Well. The organisation is pioneering the use of death doulas in the UK. "In other cultures around the globe, and for thousands of years, people have stayed in their homes to die, looked after by their family and local community. We want to see a return to this."

So how did Green become a death doula? "People sense that I am open," she says. "When I was 19, a crotchety old aunt who was dying asked for me. I could tell she knew she was dying. And she knew that I knew. She just wanted to see it in someone else's eyes – the truth of it. Then she relaxed. She was in a nursing home and no one would be open about it. She didn't like the lying and the pretending – it irritated her."

"Then, in my 20s, not long after I qualified as a nurse, I was lodging with a woman. She became ill, and asked me to go to the doctor with her. I think we both knew that something was happening. I was with her when she was given her diagnosis, and lived with her until she passed away. Her two sons, both friends of mine, had young babies and full-time jobs, so they couldn't become live-in carers. There was no question that I wouldn't do what I did. That's how I became a death doula."

Green went on to work in hospices, but found it wasn't for her. "They do a great job, don't get me wrong. I just found it all a bit holy: I'd drive home listening to thrash metal as an antidote. Some people want that, to be patted and stroked as they pass away. But others want to walk into it, to die alive – not die dying, doing as they're told.

"I've never advertised," Green says. "It's all just word of mouth. I don't always take payment, either. People want different things from me: it could be anything from being a companion at a bedside, to providing practical support for the family. Or aiding conversations with the person's doctor, which will then help with making decisions about treatment. Or navigating their way through the structure of the NHS. I've even met up with a man who simply had a fear of death. We talked for a couple of hours, and that was it, I never saw him again."

Although some death doulas have a spiritual approach, Green doesn't. "Some people will hate me for this, but so be it. If a person has not found 'spirituality' to be useful to them before they became ill, why introduce it when a person is facing death? I feel it's a way of avoiding the living person in front of you – and avoiding yourself. Providing a 'solution' to this 'problem' of death, with a story. It's big business, this spirituality. It preys on the vulnerable and it's a crutch that's going to break when you lean on it. You have your life, your living moments, and yourself – right up to the very end. You are enough – you don't need to be spiritual."

Interest in – and demand for – death doulas is on the rise. "It's because most of us would prefer to die at home, cared for gently," says Barbara Chalmers of Final Fling, the UK's first "one-stop shop for end-of-life planning". "The NHS isn't the place for that," Chalmers says. "We've lost our community doula skills: the women in the past who looked after birthing and dying. So more and more people – mostly women – are training again in these skills and offering end-of-life companionship as a service. It would be interesting to work out the cost of this for the NHS, instead of them paying to keep dying people in a ward and continuing the notion that death is a medical failure rather than the natural conclusion to life."

I wonder how someone who works so closely with death feels about her own mortality. "Death doesn't scare me because I don't know what it is," Green says. "I suppose I'm saying that the unknown doesn't scare me. I find the idea that one day I won't be here any more strange and impossible to imagine.

"But it's also a fact that I haven't always been here – I only got here in 1969. Where was I in 1968, or 1945? I have no idea. It makes me smile to think of this." So does that mean that she doesn't worry about death? "No, I don't worry about death. I worry about things like paying my bills. I wish I didn't, but I do."

So what does she say to people who are frightened of death? "I don't offer any views or advice. I don't try to prove that death isn't scary. I can't – I don't know what death is. And I don't soothe or placate people when they're afraid, but rather walk directly into the state of fear with them, as a companion, and without going into a state of fear myself. This can be done as a conversation, as a walk outside together, and often – in fact in most cases – what we talk about is not death, but something else."