Would I qualify for the NHS to cover my tummy tuck?

I hope that you have taken "mywish"'s recommendations to heart. Having grown up in London, I know that the NHS does provide coverage "from the cradle to the grave", however the procedures which are covered do have to be "functional" rather than cosmetic. In order to establish that your excess skin does cause functional problems, such as intertirgo or heat rash, in the area above your pubic brim, you will need to enlist the assistance of your GP, so that you can be referred for "panniculectomy". Panniculectomy is different from abdominoplasty, because it merely involves removal of the excess skin. Tummy tucks usually involve reshaping the umbilicus and repairing the weakness of the abdominal muscles.
Don't loose hope. In the mean time, do try to exercise, get fit and within your ideal body weight. Many insurance companies in the US insist that patients are close to the ideal body weight, as defined by BMI. Body Mass Index. Good luck.