I think you would benefit from losing more weight, however I don't personally think weight loss will cure the problem totally.
You can try the NHS route, but a lot of people have had bad experiences with actually getting the treatment....... from what I understand some NHS trusts will not fund surgery until your BMI (body mass index) is below 25, so that should be your first goal, along with consulting your GP.
I have found that weight training has actually improved the shape of my chest, and I don't think you would make the problem worse - even if you did, the effects of weight training will disappear if you stop lifting for a few months.
Total body work outs are what you need really.... try to maintain / gain muscle while at the same time lose fat.