UK person here, and someone who has been lobbied and lobbied the government on tech regulations.

firstly the amount of money that the "UK lobby" are pushing is a drop of sand in the ocean.[1]

secondly, and most importantly, the USA has no (federally robust) legal protection for citizens to guard against data collection and aggregation. So whist this is being presented as a war on anonymity lead by the dirty British, this is basically "think of the children" play for protecting anonymity. There is nothing wrong with this, its a good argument, even though its obviously flawed.

If you want to dox someone, you just need to pay the right broker. That is, in the UK really difficult. (for example flock cameras are largely illegal in the UK, certainly no council or HOA can just install them. sure you can put in CCTV, but you cannot process that CCTV to track bystanders)

There are no useful controls for citizens to limit the collection and processing of personal information. so whilst in theory you can be anonymous in america, as soon as you use a phone, or any ISP you are effectively de anonymised. I can as a company, buy your location data, tie it to your IP, then cross check with various ad networks to get usernames. (the civil legal route here is file a john doe and ask for metadata in discovery. Higher legal bar, but I don't think thats something that can be done simply in the UK)

TLDR: Contrary to popular belief there are greater protections to anonymous behaviour in the UK. Yes they have been greatly eroded, but the difference here is that there are no legal ways for companies to unmask you for money[2]. In the USA there is no legal protection for someone to share your ID for money.

[1]musk is currently spending millions propping up convicted criminals.

[2] not without your permission, or without a robust legal proceeding.