I joined the fallen livestock scheme (£10 ish to join, one off), the only time I had to call them for a dead sheep they took it the same day despite being based 2 hours away (they are the nearest!) and it cost less than £10. No hunts round our area, so thats not an option. Again I wouldnt eat it unless it was both an accidental death and I saw it happen - even then you still have the prob of how to dispose of the head as that has to go as special waste, which Im not set up for, so still prob would go for the FLScheme.
I didnt have to be in either, you pay in arrears by DD, so was able to leave it in loader bucket for them to take and they left the paperwork