Key difference is with the companies you have mentioned (River Island, Arcadia, Timpsons) is the jets are not owned by the company - but (through "shell" companies) by an individual - normally owner/CEO depending on the company.
Now, a company using a jet owned by a third party and not on an AOC or similar would probably constitute grey charter (depending on the circumstances, etc) but why let the facts get in the way of a good story
