I've lived in various countries and the UK is the only place where people would bat an eye an nakedness.
I'm currently in Korea, where spas are very common. A spa in Korea is very much a naked thing, and people of all ages go. The old women scrub each other down, every single inch of their body, and I mean EVERY inch.
Groups of same sex friends in there totally naked, just hanging out. No big deal.
Last time I was there, a group of British girls came in and refused to take off their towels. They were shouted at pretty harshly because it is just not the done thing. They were causing a massive fuss, going on about how mortified they were, how they just couldn't be naked in front of each other and I just...ugh. Who cares? I'm fine with my body. Not perfect, but I have some scars, some hair in places I can't be arsed dealing with...same as everyone.
The Brits really need to get over this attitude if they're gonna go abroad and go to spas. If you can't handle being naked, then don't go to a spa.
And as for being naked in a changing room...how else are you supposed to change???