1) this would mean that the government (executive) would need to bring in primary legislation to allow EU citizens to continue to work and live in the UK. (those who have registered I think would be ok. I'm grateful for corrections on this point though) This is something they have promised, but not actually delivered (Which I suspect will be running theme.)
2) haulage companies would need to change drivers (and probably truck) at the border (possibly the EU side, which would be interesting, as I'm not sure how haulage licenses work in practice. I know multidrop/mixed purpose [as in deliver x and pickup y are expressly not allowed])
3) as far as I'm aware, any truck driver delivering stuff would need a temporary work visa, which requires a sponsor and load of cash and time (The first is difficult, the last in very short supply.)
If anyone has links to legislation that contradicts this, I'm all ears.