Use a little bit of critical thinking, please. Here, I'll help you...
Whether it works or not, the government proclaims it a fantastic success, and says that it's now going to require it for other age-gated services - probably starting with gambling, "to save the children", along with a glut of headlines about how online gambling is a scourge amongst the young. Again, just like porn, Mumsnet and similar sites will erupt with support for this fantastic measure. They change the to let them hang on to the identity data "for security purposes only", requiring a warrant.
Then..."social media is harming our children!", they bring in laws to prevent anyone under 16 accessing social media, and...oh look, we've got this great way to verify people's ages, facial scanning! Now, the #1 primary use of the Internet amongst 16-24s also requires facial scanning, fully supported by sites like this because "save the children!". At the same time, they require a legal licence for the distribution of VPN software, and require all VPN providers to log and track site access against users with the same justification, and they have to report all users' traffic habits to the government.
Quietly, in the background, they slip a change to allow "limited sharing of identity data amongst government departments and secure partners" into an unrelated law (that kind of wording already exists in the statutes for identity data, by the way, but they have no way to collect it at scale). Now they have linked identity data on the majority of UK citizens in that age bracket, which (over time) will increase to cover the majority of the entire population, forever.
Now, since most people have got used to the idea, they add it to the authentication process for accessing government services online as a convenience measure, optional at first and then mandatory after a few years.
And that, ladies and gentlemen, is how you go about removing an entire country's privacy and anonymity on the Internet.
Don't believe it could happen like that, because people aren't stupid enough? Look at Brexit - sold to the public (successfully) as a way to stop the immigration problem and our flagging economy, both of which have only got worse (with no improvement in sight) and turned out to be a massive act of national self-harm which is still supported by huge numbers of the population despite delivering none of the supposed benefits 7 years down the line.