The BL is not after my site specifically. It is after all sites it "sees" as "UK sites". All I am asking is a definition of what is a UK site.

I am asking for such a definition not because I object to archiving but because placement of my site into a collection of "UK sites" is an obvious mis-classification.

However, it may be and in most cases is probably still copyrighted (with some exceptions such as US government content). Archiving is probably OK in most cases. Making that archive available to the public (e.g. Wayback Machine) is something that gets a blind eye turned on but there's probably not much legal backing for that--and which, to date, pretty much no one has wanted to try to build a legal case around.

It's not legal in the UK to make a copy of a website except if you're a deposit library and the website fails within the strictures of the Legal Deposit Libraries Act 2003.

But, under that act, if it's hosted in the UK then BL can make a copy (for access in person by someone visiting the physical library).

UK law is pretty draconian, in my personal opinion, when it comes to copyright.

Of course that's true.

But it's still bizarre for a legacy entity like a nation state to presume that it can identify an internet phenomenon without first explaining what it even means when declaring its intention to do so.