What sort of things were you thinking of using your US insurance for in the UK? If your routine medical things are covered by the NHS, then you can have them done in the UK and won't need to pay much (if anything) for them anyway.
I do understand that. It's just things like eyeglasses, dental work and orthotics that I'd rather do in the US. I know that pretty much all of those things would be pretty cheap here, but I feel like dental care at least will be of better quality in the US and, even if it's not, it will probably be less of a hassle since I really like my dentist there and have had a couple cosmetic issues. Also (and most of all), my parents will pay for my medical care in the US. Free is better than not much.
So, what I'd really like to do in the US is the non-essential stuff. I will, of course, use the NHS to have a regular GP and won't wait to go to the doctor until I'm in the US, but the things that are just kind of luxurious (and that the NHS wouldn't fully cover anyway), I'd rather just do with the doctors I know. Of course, if my insurance covers anything over here (which I'm pretty sure it doesn't--just waiting for an email back from them), I would be quite happy to take care of everything here and be able to just relax and visit friends and family in the States without always having to jet off to a doctor's appointment.