The state isn’t totally incompetent but doing it properly would be a serious undertaking, the kind of thing where the recent track record of big government tech projects isn’t great
If you want to really make sure nobody in the uk can easily access 4chan (PRC style) it needs some effort, and you're in an arms race with attempts to mask/tunnel traffic so it gets through
One example is after the Southport riots, miraculously the justice system became hyperefficient and the perpetrators were found, arrested, charged and jailed within a week.
That suggests a lot of what looks like incompetence (potholes, petty crime, maybe also this) is actually just the state not really caring about a lot of issues.
If they decide they really care about internet censorship, I wouldn't rule out them suddenly becoming a lot more competent in that specific area