If it comes to having the same legislation in the UK, it'd likely ban decentralized web as well, perhaps requiring submitting your ID upon connecting to Internet every single time.
Especially with the way we are moving. Most people today are happy to use sso with services like facebook or google. Most people also have their real identify tied to their core profile they use to sign on to other services. The abstraction between the internet and the cloud is becoming more blurry to a internetizen that is technologically ignorant.
Practically the only way of connecting anonymously to the Internet is the old-fashioned wardriving, or getting lucky and finding a "free wifi" which is not limited to the Web only.