if I had a child, I would ask the child first, although if they were overweight and old enough to understand, /not excercising and not eating healthily dispite my discussions with them, I may reconsider this if I had tried everything first.
I dont see why they need so many details, the school they go to should be enough, that would worry me if the details get into the wrong hands like so many other government c*ckups!
I am not sure about having it done so young- kids grow fast and one week can seem obese, the next have had a growth spurt, its hard to know if your child is obese, underweight or just growing, even the medical people dont ever really know, they compare with general statistics but as with gowing, things can change fast so comparisons dont really work.
I would be om with giving these tests a go but if I knew my child had a problem with food/lack of excercise and wasnt doing anything about it. Kids need to be kids but once they get too old and stop doing as you ask them (eg not eating £1 of penny sweets everyday!) then you need to communicate the importance of thier diet and excercise to them in another way. I would recommend this if they were really not living healthily and were eating too much junk food/refusing to excercise and over 7 or 8, or if they were over 13 and only then under strict confidentiality, at the doctors and with support offered before they try and "celeb" diets or takeing up an eating disorder.
The government have a duty to act as its the rest of us that have to pick up the NHS bills for stomach stapling and eating disorders, but the parents should always be the first port of call on a childs upbringing, not the state, school or doctors.