I have a feeling that any livestock must now be transported in a proper livestock trailer - DEFRA rules. I know moving my goats, and the sheep was a nightmare with movement papers, and cleaning trailer out before and after, and that was just moving to a new home, so can imagine going to the slaughter house is no different.
Someone told me they tried to bring a couple of lambs back from the market and were just putting them in their van, and were stopped. They got someone with a trailer to take them from the market, met in a layby and popped the lambs in the van. I would imagine that happens quite a bit, but its if you are caught.