Individual sites already do censor, but I don't picture us having any kind of government-level censorship of the internet the way China does, for example.
I'm not sure of the status of this or when it is intended to take effect but the UK Government is intending to try to make "social media" sites ask for proof of age, possibly via a subscription system, to try to reduce the amount of pornography easily available to children. Whether it will work, is another matter.