Almost a quarter of British women are obese, and nearly as many men, according to the European health interview survey published by the EU's statistical office Eurostat. Meanwhile, Jamie Oliver continues his campaign to improve school food, asking the prime minister to ensure that academies don't undermine it, and again focusing on "rocketing obesity rates in the UK".

But we're getting the focus wrong. Obesity isn't what's robbing us of good health and life. Using data from the Cooper Centre Longitudinal Study exercise scientist Steven Blair and his colleagues have established that you can be fat and fit. It is better to be overweight and active than normal weight and sedentary in terms of risk of mortality, the research has shown.

Blair calls physical inactivity the biggest public health problem of the 21st century. Yet instead of paying attention to our sedentary lifestyles, we keep on focusing on fatness. As individuals, we just can't resist stepping on the scales and it's a staple of weight-loss programmes. Physical activity is almost always a secondary consideration, and then only because of its power to help us lose weight. This narrow focus is repeated in campaigns and the media, but the obsession with how much people weigh and how much they need to lose just isn't helping us lead longer and healthier lives, or reducing the burden on the health service.

Campaigns such as the government's Change4Life initiative combine diet advice and alcohol tracking with activity suggestions, but the message needs to be far more straightforward. Forget berating young and old for their eating habits and what the scales are saying, and give them the much more appealing solution that physical activity is the way to a longer, healthier life.

If you offered people a drug that would confer these benefits with no side-effects, you would be trampled in the rush. A pill that promised the same effect as just 30 minutes of moderate intensity activity each day would make headlines around the world. Yet because it's not a new miracle cure on the market, and it's not a mythical superfood, it's not news at all. But the evidence is there. Physical activity can reduce the risk of heart disease, type 2 diabetes and some cancers and even delay cognitive decline. According to Karim Khan, editor of the British Journal of Sports Medicine, you probably need to be doing 60 minutes a day for optimum health (after which time there are diminishing returns health-wise). If we're going to pick a health issue to be fascinated by, isn't this the one?

It isn't about getting everyone running marathons, or setting aside the time and money they don't have to go to the gym every day. For many, these are the unattainable goals that lead to a sense of failure, and send us right back down the cul-de-sac of putting all the emphasis on losing a few pounds because a pleasing result on the scales gives us a moment's relief from our internal nagging, and that of society as a whole.

Instead, we need to put back the activity that modern life has removed into our daily routines. Making up our half an hour of not being sedentary does take an effort, but at least it can be achieved in manageable 10-minute blocks, can be made part of life without having to find fresh hours in the day – and above all has the merit of being in our control. A positive goal is always going to be far more attractive than nagging people about their eating habits, or pointing out the excess flesh.

The narrow focus on obesity for government, for campaigners and for individuals needs to change, and if we just can't quite get over our obsession, at least stepping on and off the scales still counts as activity if you do it enough.