The CAA don't have enough resources for complete regulation and I suspect that the AAIB will recommend the CAA make improvements in the way such flights are controlled.
Whilst I agree with the intention of this point, I don’t really see how they can do that in practice.
If the conclusion that many here have reached that this was a good example of an illegal charter are right (and I have to say that I am one of them!) then just making another rule won’t stop the next person willing to break it, and I can’t see an inspector interviewing the pilot of every aircraft departing with more than one person on it.
Realistically, the only practical (but not easy) solution is to identify some individual bent charters and come down on the pilots involved, and those organising or facilitating the flights, like a ton of bricks and invoking sanctions that are a true deterrent in a very well publicised way.