In one short week, the BBC's Great British Class Survey has entered the annals as one of the most successful pieces of popular sociology ever conducted. Launched only last Wednesday, its Class Calculator has been uniquely visited 4.8m times. It was the second most popular story on the BBC website this year. The research was not only featured throughout the British media, but has also travelled globally; one million visits to the Class Calculator are from people outside the UK. The topic of class has – if only for a brief while – permeated popular conversation. My 13-year-old son told me that one of his school friends had found out that he was in the precariat – precarious proletariat – category (sensibly, my son advised him that this was because he probably wasn't earning any money yet).

As an academic sociologist, this take-up, while exciting, is also disconcerting. I am more used to debating social class with my academic peers than seeing the topic taken up so actively in the public arena, and it has been subject to much biting comment. We are deluged by emails complaining about how the calculator puts you in the wrong class, with the wrong labels. Eminent sociologists such as David Rose are concerned with the quality of the social science lying behind the work (do we really need Bourdieu rather than Weber?). Guy Standing is not convinced about our use of his "precariat" (precarious proletariat) term as the label for the most disadvantaged class that we uncover. There are already numerous spoofs and take-offs of the class model and its measurement. Given this furore, I want to explain what we are trying to achieve sociologically with this project. Is this a model of a new kind of accessible social science? Or is it a worrying case of pandering to media headlines?

We are relaxed about people having fun "placing" themselves and discussing this with family and friends, and arguing with us sociologists along the way. It has led to a wider collective discussion on Twitter and Facebook, which we see as a desirable resource for a public-facing sociology in a digital age. We do need to set the record straight, however. The Class Calculator was designed by the BBC to mimic the more complex model we had developed on the basis of the survey data, and the two should not be conflated. As numerous people have pointed out, changing just one response can shift you between different classes. This would not be possible within the latent class analysis we deployed, where all six measures are simultaneously used to allocate class membership. Actually, this kind of simplification was deliberate, as the measures used in the Class Calculator were chosen precisely to make respondents aware of the most important factors in placing people into classes. But it still poses questions about whether we have been simplistic.

Let me be blunt. The concept of class matters, because we need a way of connecting accentuating economic inequalities to social and cultural differences which permeate our society. Rather than seeing our lifestyles and social networks as somehow separate from economic inequalities, there are overlaps that can work together to produce social advantage and disadvantage. For all its problems, the concept of class remains fundamental to making these connections. Sure, we would all rather not live in a class-divided society. But in reality, the markers of class cannot be doubted. Our model seeks to find a way of making these connections, arguing that occupational measures alone are too blunt a tool for this purpose.

Of course, the definitions we used are a matter for debate. Labels themselves convey symbolic power; we are not naive about this. We have followed with great interest in recent years how terms such as the "underclass" or "chavs" have been bandied around, and how "symbolic violence" (to use one of Pierre Bourdieu's favourite concepts) has been done in their name to denigrate certain kinds of people. This is precisely why we were concerned to focus on the wealthy and powerful in our analysis, and also to challenge the use of the "underclass" label to categorise the poor and disadvantaged.

In my view, probably the most important finding from our research is the existence of a distinctive "elite" class. We are so used to turning the telescope on the poor and disadvantaged that sociologists have had little to say about those who are at the apex of British society. Sociological studies of class have no specific place for an elite category. What we have shown is that this very wealthy class is now clearly distinguished from all the other classes in Britain, and the economic differences are huge. That is a powerful and unsettling finding.

Because of the sample skew of the Great British Class Survey towards the well-off and well-educated, we have an unusually detailed data source to understand the upper and middle ranges of society. There are several thousand chief executive officers in the sample and large numbers of graduates from different universities, so that we will be able to unravel in unusual detail the precise processes by which social closure operates.

Some say we have taken attention away from the fundamental divide between "middle" and "working" classes at the centre of so much of our thinking about class. This was our way of trying to recognise that older stereotypes of class don't do the job any more, and to recognise the fragmentation of classes in the middle ranges of society.

As Martin Kettle observed last week, there are numerous points of detail to discuss and contest. But, like him, we are confident about the headlines. Far from Britain becoming a classless society, as Margaret Thatcher and Tony Blair both claimed some years ago, we have seen the reworking and consolidation of new kinds of class inequality. In the politics of austerity which characterise our times, this needs to be recognised. Hopefully, the Great British Class Survey has helped us to do this.