Opinions on this subject and the whole Olympics issue with aviation is like the proverbial asshole, 'We all have one'.
Which one is right? Who knows until something or nothing happens?
Please tell me on what basis I am obligated to complete a GAR form and provide it to a hotel when my flight originates and end within the United Kingdom and does not cross an international boundary ???
Of course you don't have to provide a GAR to a hotel. As far as I grasp from your first post, the hotel you went to has simply been asked by the Police to keep a record of movements. Besides for flights within the UK there are indeed times when you do need to properly file a GAR.
Just because you don't have to do something doesn't mean you have to go out of your way and even upset people by making a point of not doing it!