Though, that does go back to what others have said - It absolutely depends on how much your dumping.
It's a "system" that we've "gotten away with" for the last 25 years.
For us, general refuse - A bin bag of recycling and a Tesco bag of rubbish every week is easily taken home by the OC or other staff and thrown into our own bins without issue.
If we clear out the stores or something then it's a one-off day of trips to the dump. Easily sorted.
Whenever we've had anything really big to clear (about twice in the last 20 years) we've gone via wing and SERFCA have hired a skip.
One would have to be regularly dumping a shed-load of junk to warrant a Waste Carriers License or to get into bother by taking it to the amenity tip.
This has to be aimed at higher levels than the average Sqn.