Everything that is not prohibited by law is permitted and is 100% legal.
The Denmark route is 100% legal. UK C&E don't like it but they can't stop it - it is for Denmark to have chosen this particular interpretation of the EU VAT directive and once they have issued a certificate of free circulation then that's as far as it goes.
But it has to be done correctly. For example, you can't fly the plane around the UK (at all) prior to it going to Denmark.
A&C - I had the same experience, and had no problems after describing the business and supplying the business plan. But in retrospect it was barely worth doing, for the hassle. However, when I did all this, the Denmark route was not a well known option.