Technically in the UK, livestock should only be moved in something that can be completely disinfected. So unless you wanted your car or whatever sprayed all over by a power washer with disinfectant, then they should be in a trailer. We actually also travel goats in the van, but obviously the back of that can be washed out and disinfected.
That said, I know people who have travelled goats etc in the back of cars. I remember going to market as a child, and coming back with a calf in the back of a hatchback car.
Beth