Today marks the start of "Dying Matters Awareness Week", an annual campaign supported by the National Council for Palliative Care. The hope is to get people talking and thinking more about death – about how they, and their loved ones, might have a "good death".

The idea of a good death is not new. Anthropologists, historians, and other social scientists have long documented the variety of ways in which a good death is achieved. Crucial to this is not only how someone dies, but how that death is commemorated. In many cases, to include Britain today, a good death has to involve a good funeral. Ritual, even in this postmodern age, is flourishing. And whether or not we identify as religious such ritual, it seems, still counts.

I spent last year conducting an anthropological study of the British Humanist Association (BHA), an organisation which on first thought might not bring to mind a commitment to rites de passage. For the association, however, providing funerals to those who do without God is a major aspect of its work. There are close to 300 humanist celebrants, and they conduct more than 8,000 funerals a year. It's a burgeoning service. As Linda Woodhead noted here last week, "the churches' hold over birth, marriage, and death has weakened dramatically". According to a major study by Co-operative Funeralcare, in 2011, 12% of funerals in Britain are now humanist or otherwise "non-religious".

As an anthropologist, one of the reasons I wanted to study the BHA is because of this commitment to the experiential and embodied side of being non-religious. As an increasing number of philosophers within the atheist and humanist ambit have stressed, much of the god debate over the past six or seven years has been dominated by a hyper-intellectualised version of what it means to do without Him. But godless dons have funerals – most of them do, at any rate. And so do other non-religious people.

To be sure, a good BHA funeral is a carefully scripted event: words matter to the celebrants, and ought to "capture the person", as some of the celebrants put it to me – and as I learned the hard way, training to become a celebrant myself. (As an anthropologist, I had to go native as much as I could.) The scripts I wrote during the training – a three-month process – were deconstructed by my teachers, word for word. I felt like a student all over again. Yet humanist funerals are also, like all rituals, carefully scripted performances: sensuous events in which the semantic content of what is said is often eclipsed by what exists beyond language.

While much of my time studying the BHA was spent in the offices at Gower Street – where Darwin Day lectures are planned, and where the staff and interns work on the association's various campaigns – much of it was spent with the humanist celebrants in their day-to-day work. It never got them near Bloomsbury. Celebrants spend their days at council-run crematoria and cemetery chapels, or meeting with the families they serve – be it on a council estate in Catford or a semi-detached in Teddington. Indeed, when it comes to the ritual arena, humanism's reach extends well beyond the university-educated middle class.

Many of the families that humanist celebrants serve have no idea what humanism is, and many don't really care. What they care about, often, is that Uncle John didn't go to church and didn't want his funeral taken by the vicar. Even more so than when we wed, when we die there must be fidelity to an inner self. Going through the ritual motions (what a telling phrase) is less and less an option.

"Capturing the person" is often a concern within religious funerals, too. I observed almost half as many Christian funerals as I did humanist ones; the Beatles get played at both. Capturing the person is a distinctly modern phenomenon, however. And it sits at odds with much of what we know about the nature and function of ritual. For most of the historical record – and even in many situations today – the point of ritual has usually been to minimise the significance of the persons involved and maximize something else, whether that is the power of a transcendent God, or the monarchy, or the importance of some other institutional or social role. The idea that a funeral should include the person's favourite Beatles song signals the move to a new cultural frame of what constitutes a good death. As ever, it is in the ritual process that we often find the best sense of our values and social makeup. And in our rituals of death, we get a particularly good glimpse of the post-religious, post-secular condition.

• The BHA study was was funded by the Economic and Social Research Council