The thin end of the wedge.
Blocking websites is censorship, it doesn't matter what content is available through the site. This applies to all websites regardless of illegality.
If a website is discovered to be making illegal content available it should not be blocked. It should be shutdown as soon as is possible.
There is a problem with this though. The Internet is global and what is legal in one jurisdiction may a carry a death penalty in another.
The Internet cannot be policed. It can only be censored.
Many extremist governments currently censor the Internet. They want to protect their citizens from content that is illegal according to laws that the majority of those citizens support and offensive to the culture of those same citizens. This maintains a status quo. No one thinks, no one gets new ideas, no one crticises, the culture is safe, static, closed and unchanging. Knowledge and progress is static and unchanging.
Freedom of information is dangerous not only to the the consumer of illegal content, in the form of punishment for consuming. It is also a threat to the Status Quo. People in ignorance without critical thinking live in static societies that are very slow changing. When those people are exposed to ideas and information from others in less restrictive, less static societies, societies with critical thinkers and they start to think outside of their culture, beyond their peer set boundaries and indoctrination, they start to criticise and want change, they see it as progress or a new freedom.
When compared to those extremist governments that currently censor the Internet, the UK has been pretty much free of it.
The UK prior to this law censored illegal sites through Internet watch: http://www.iwf.org.uk/
People would hopefully report illegal content and it would be blocked.
With this new law real censorship begins. Sites will no longer be blocked only because they provide illegal content, they will be blocked if they are found using "abhorrent search terms".
Now who decides what is abhorrent? Somebody who has lived and survived the school of hard knocks or someone that has been pampered and protected from suffering and "bad influences", someone who cannot think beyond their own indoctrination? And how does the algorithm that detects "abhorrent search terms" decide that you were searching for what is genuinely abhorrent and not because it appears so from the words involved?
Then there is mission creep which search terms next and for who's reasons?
This is also unworkable and so easily bypassed as to be pointless political gesturing as far as protecting children and the vulnerable. As a method of censorship introduced under the guise of distasteful porn filtering, censorship becomes acceptable and the norm. The UK gov want to maintain the status quo, restrict your access to information, stop critical thinking and take us back to a middle aged static society. We will cease to progress if we cannot share information and through criticism of that information gain truthful knowledge, no matter how abhorrent that information might be..... to someone.
EDIT: made a bit more coherent.
Children of all races, creeds and nationalities will happily play together, until an adult tells them lies.... Indoctrination the only legal form of child abuse.