Do all British TV shows have this much nudity?

Find me a single British show with as much nudity/violence as virtually anything on HBO, Showtime, Starz etc. The network channels are only a tiny part of American TV - overall, there's actually a lot more freedom of content than virtually any other country I know of (I work in TV, starting in England, now working in LA).

And actually, America has no censorship body. That's why movies don't get banned here, and are generally available in their uncensored format unless the filmmakers decide otherwise. The worst you can get is the MPAA giving you a restrictive NC-17 rating, but even that's becoming less of a problem now that there are so many other ways to get your film out there. Subscription TV, like HBO, Showtime and now Netflix, Amazon etc., can technically show whatever they want provided it's not illegal (child pornography etc.)

The same can't be said for the UK, where the BBFC has to rate everything that's broadcast or sold (including special features on home video, which is why R2 releases are often so barebones in comparison) and has the power to cut and ban things altogether, which it still does a few times a year. In the US, the MPAA can't cut or ban anything, they only give suggestions to producers for what to remove if they want a lower rating.

Put simply, the grass isn't always greener.