I don't think it will take long for most people in the UK to realize what's going on, they're already protesting, and it's clear that protest footage is being blocked too.

I also don't think it would take the UK too long to block sites like what you're describing. It's now totally doable that ISPs would run non-whitelisted websites through an AI screening before serving them to the user. Or they might choose to go after individuals accessing them multiple times, as repressive governments go after individuals possessing/viewing politically "harmful" material.