Copyright claim to Bitcoin Whitepaper
Disclaimer: IANAL, this is not legal advice, the following are some lines of thought that I've seen on the matter that seem plausible to me:

The original client was published under MIT License. The whitepaper was packaged with the original client. The license statement explicitly covers the &quot;included documentation&quot;. It seems plausible that the whitepaper therefore was published under MIT license.
Just mentioning bitcoin.org on the whitepaper does not transfer the copyright. Transferring copyrights is a rather involved procedure, and generally copyrights always remain exclusively with the actual creator. The inclusion of the URL in the document's header could potentially be interpreted as consent to be published there. I would expect 1. and 2. to be subject of the lawsuit.
I don't have any special insights why the copyright claim would be pursued in England. Potentially, the laws are favorable to the endeavor, or it's simply due to the claimant residing there.
If someone were to establish themselves as the copyright holder, they could potentially deny some parties from publishing it or use the copyright to legally pursue some parties. More likely, it would be used as evidence to cast the claimant as the creator of Bitcoin in the eye of the public, or as means to enforce patent claims.
I'm not aware of any special statements by Satoshi Nakamoto regarding the status of the Whitepaper.

Earlier, a cease-and-desist notice was sent to Square (among others) on behalf of Craig Wright for hosting a copy of the Bitcoin whitepaper. The Crypto Open Patent Alliance (COPA) responded in February 2021 on behalf of Square, requesting that the copyright claimant substantiate the basis of the claim. After no response was received, COPA announced filing a lawsuit alleging that CW in fact does not hold the copyright in April. I am optimistic that this lawsuit will clear up the matter.