The publicity for Learning How to Die tells us not to be put off by the title. That is perhaps understandable. Although death is less of a taboo subject than it once was, a recent poll found that the majority in the UK fail to set down their wishes for end-of-life care, make wills, register for organ donation or organise life insurance. Death is something we try to ignore.

As far as I was concerned, the title was intriguing, not off-putting. As I sat in the compact Burton Taylor Theatre, I looked around to see a wide range of ages present in the packed audience. As we all settled down in our seats, on stage Luca Rutherford loosened up, smiled a lot and ambled around the stage waiting. I couldn't help wondering why she – with youth on her side – should be so fascinated by death. At her age, I certainly wasn't.

Of course, by the end of her 55 minute show, it had become clear. Few of us remain untouched by death and she has had her share – a father with cancer and the sudden death of a friend.

She tells the two stories simply, sometimes as herself, sometimes as a dispassionate narrator, and sometimes via the recorded voice of her father. Alongside this she ruminates on life and death and how we should treat those two aspects of our existence.

She starts the show with statistics: there are currently 56 million deaths a year, which apparently breaks down to 108 a minute or 1.8 a second. But that is all they are until death impacts upon you personally. Death is inevitable, yet we are programmed, Luca suggests, to forget that uncomfortable fact. But if we were to face the truth that life – our life – is finite, how might that affect how we live? That, I think, is the thought that Luca wants us to take away. Whether we consider life after death an illusion or not, she wants us to live life well, whatever that might mean for us as individuals. She wants her £5 donation to Oxfam to achieve something, however small.

Despite the subject, Luca is a cheerful and earnest guide to death and life. She is, I think, still trying to come to terms with both those states. As, perhaps, we all are.

The small theatre was packed. So if you fancy going to see it, get your skates on. Learning How to Die will make its mark on you.