The NHS use centile charts from several decades ago (when people were, on average, a healthier weight), which is why such a large percentage of children are now above the 99th centile on them.
I used to work in this field and it's scary how out of touch society is with what a healthy weight 'looks like'. I regularly worked with children who were above the 99.8th centile, (effectively unplottable on the charts) with a future of diabetes and serious health problems ahead of them, and yet parents just thought it was a bit of puppy fat. Of course, there will always be the exception of children who grow out of it, and that's great, but many, many don't. My issue is not with BMI tests, but with the inadequate provision and follow-up support for families who are told their children are obese.
Yes, BMI is a blunt, imperfect tool, but it is difficult to roll out national schemes to identify and tackle obesity without it. Parents are usually in denial, and health professionals don't have time, impetus or are afraid of offending, to address the weight of children.