None of the methods described here and elsewhere enable changing a location. I was comfortable with my ISP location being displayed as my location. I restrict locations as far as possible as a matter of course.
I upgraded to Monterey a few days ago. I noticed the default location had changed to SE1‡‡. And I was being asked to allow this address(?) in order to process with Apple ID two factor authentication. I called this off and attempted to find the reason. Apart from the usual, and ineffective, stream of suggestions there were a number that suggested it should be ignored and allowed.
This I did and I continued without a hitch.
However, in the absence of an acceptable answer from Apple tech and my curiosity I chased down the code. For interest the "cross of Lorraine" symbol ( ‡) is found by keying "Shift+Option+ 7".
Hey presto... the designated location is an Apple repair shop in an inner borough of London. Also the associated map is listing a number of similar Apple outlets in central London. None of which I have ever contacted from my home, some 100+ miles away.
And now in standard searches, on various browsers, this Apple generated location is flagged as my location on all my devices!
So now I know the source of the changed location I will ignore it, as before.
Sadly I expect this will be another incongruous item that Apple will not fix? ....or Explain.