There is no need to access the "dark web" to view any of this stuff.
The things you allude to earlier, Brazil's Twitter block and so on, are relatively simple to engineer because it's one singular domain. It's also simple to circumvent, but it's effective enough in preventing the most rudimentary ways of accessing that site from functioning.
Blocks on specific content only work if you know which sites the content appears on, and unfortunately, for every obvious candidate like "Pornhub", there are thousands of lesser known pages that still show the exact same content, that can still be accessed freely, and will continually evade all attempts to block them. So yes, you might restrict the ability to view that content on some pages, but it's still going to be easily accessed on others.
"Bans" and "blocks" on internet content are totally impractical, will never be comprehensive enough to actually prevent access to content as intended, and even the most draconian ones still do not prevent people from accessing what they want to access. China is notorious for State policing and censorship of the internet, but people in China still routinely view the exact content the Chinese government is going all out to prevent them seeing. Sledgehammer approaches to policing the internet simply do not work, because the internet can not be policed effectively due to it's very nature.
Much of the content that is supposedly "blocked" in the UK is no such thing, and no, you don't need special browsers or clients to access it. ISP's pay lip-service to government demands, but in reality even the government understands that it's impossible to force ISP's to censor the internet on government's behalf, so they'll make a half-hearted attempt to restrict access to the most commonly sought domains, while doing nothing about the hundreds, or thousands of others which are just as easily accessed and host the exact same "blocked" content.
You can petition all you like for bans and blocks, but the reality is, no single government has the ability to enact any effective block on content due to the fact it can not control how and where that content is hosted, and they also have no ability whatsoever to force compliance from any host, operator, or user outside of their own legal jurisdiction, so in the meantime, the only thing that can really be done is to more heavily restrict, monitor, and police children's internet usage, even if that means removing their access to smartphones and so on.