Free speech (as in the first amendment) allows you to say most things, it does not however compel others to broadcast or host your speech. So there is no free speech argument for a service provider to be required to host your website or protect it with a reverse proxy.
You can speak, but nobody is required to give you a megaphone and nobody is required to listen.
> there is no free speech argument
You really mean there is no first amendment argument. There is still an abstract free speech argument.
Another example: SLAPP laws that effectively intimidate people into silence are a free speech issue but not a first amendment issue.
Further, if SLAPP laws did burden speech, then that would be a first amendment issue since they are enacted by states which are bound by it.
Just because companies are legally allowed to remove content (e.g. the owner of Twitter removing content critical of Tesla) does not mean there are no free speech issues. That would be like saying there are no free speech issues in China as long as you follow the law.
Further, just because the law says a thing doesn’t mean I have to agree with it. Laws have legal authority not moral authority, so even if a company is legally allowed to do something doesn’t end the conversation.
I'm amazed that this can happen so easily in the US. I realise the US courts probably don't care about UK citizens, but free speech is free speech. I realise that's not without consequence, there's been nothing untrue said about this individual to warrant this action.
From what I understand anyone in the UK can make claims, file cases, etc…, against anyone else.
Edit: They may take action in another jurisdiction where they posesss some advantage, but it would have to be taken up in UK courts to actually mete out formal punishment.
How is that relevant when they would still need to go to a UK court to go after you in some way?
Which is what you are afraid of, I’m assumming?