Prompted by the reply (MacInTouch on pause - #43 by macintouch.com) from Macintouch, I followed his link to IP Chicken. It gave my IP address as xx.yy.30.131. I then went to whatsmyip.org (which I’ve used for years), and it gave my address as xx.yy.40.143 (the xx and yy parts were the same). Revisiting the two sites gives the same results.
Curiously, although I verified the discrepancy I wrote about repeatedly over some 15 minutes, it’s now gone away: all three sites now show the same (very different) v4 address. Only the one @Shamino suggested realised I am using iCloud private relay.
That site gives my v6 address but not v4, and gets my ISP wrong. It also puts a US flag next to each line of output, for reasons which are obscure (I’m in England).
That site isn’t doing what you may think. It is not attempting to match an address to a location (e.g. a Whois lookup to determine the owner of an address block).
It is using the global BGP routing table (used for routing traffic between all the separate networks that comprise the Internet) to determine which Autonomous System (AS) your address belongs to. It then presents who owns that AS.
Due to the complexities and business realities of how the Internet operates, a single AS may (or may not) span across multiple nations, owning registered address block in thousands of different locations. And address blocks may advertise connectivity via multiple AS’s.
So it’s not surprising that in your case, your address block (almost certainly registered to your English ISP) is part of an AS that is owned by a US company.
In my case https://whatismyipaddress.com/ is giving me the correct Internet service provider and IPv4. The IP I have confirmed by looking at my Apache access log.