if the insurance company got a skip then they should also be paying someone to pick up the rubbish and take it to the skip...
I'd have a word with the insurance company steve, see if you can get something in writing to show to the sh't police if you get stopped, something that covers you under their umbrella so to speak, but if they've just got a skip and no waste carriers licence you wont be covered either... sounds to me like theyre expecting you to cover it for them..
coucil jobs had a bloke with a flat bed tranny, we just left all our crap in rubble sacks just inside the garden fence (not on the highway - important that) and he came round once or twice a day and picked up all the crap, carted it back to the yard and tipped it into a mix of skips, once he'd stripped any metal away of course....