I'm going to guess that many readers from this US-focused site have assumed this is like the ACLU or something but for Britain. It er... is not.
It's a platform for Toby Young in particular, and a cadre of fragile Right Wing "intellectuals" to insist that it's wrong for anybody to even criticise their bullshit.
This gives you some sort of idea: https://www.vice.com/en_uk/article/4agqbn/toby-young-free-sp...
I actually clicked this link before noticing the affiliation, because I thought it might have technical content and that would actually be interesting. It doesn't.
So, ignore Toby Young, but as usual for HN people probably aren't much interested in the actual article so much as the headline anyway, here's the technical consequences of the "plan" if you want to call it that.
This government (and its predecessor) have a core plan that relies on how the Internet worked in like 2016. Much of what people do is unencrypted and even when it's encrypted you can at least identify who they're talking to. So your backstop is that if sites are unco-operative (and we can assume many actively criminal and terrorist sites will not cheerfully co-operate) you block them in DNS. This is a known quantity, you can buy DNS blocking appliances at ISP scale. You can budget for it. The service providers will want so-and-so much money, you make them pass the cost on to their subscribers, hopefully it's not enough to cause push back that loses too many votes.
However even this limited plan isn't actually popular (it polls badly with certain groups and it's too technical for your doorstep representatives to have any hope of justifying their position so best to shut up about it) and from 2016 onward the British government has had plenty of more important things to do. This plan keeps getting kicked into the long grass. To be clear: It's a government plan, the government could make time for it on the legislative agenda, this isn't like a US House bill that Mitch won't even read let alone bring to a vote in the Senate - but they are far too busy to prioritise this.
Meanwhile it is now 2020. Meanwhile DPRIVE is deployed and ECH (what was once eSNI and now encrypts more stuff) is starting to shape up. So the DNS blocking strategy doesn't do anything any more. Now you'd have to rewrite the plan, invent new ISP-scale blocking appliances, goodness knows what those cost and what other problems they introduce, and you still haven't even tried to see if your plan does anything, much less achieves whatever nebulous goals are in your current white paper.