Private coaches were a rarity in Britain (I think you needed an act of parliament to have one); the exception is the royalty. Actually, the royalty technically didn't have their own cars; the government owned them and the king and queen paid a "fare." Probably no one else used them. Here's a set of photos from what the Museum calls the "jewels of its crown" -- cars retired from transporting royalty that the museum signage calls palaces on wheels. (Obviously, they haven't visited RV display lots lately, but this stuff is not really trailer trash).
The private car (really a set of cars each for a dining room, living room, and bedroom) were the lavish equivalent of today's private jets. This page contains several photos made by poking the camera through the windows. Visitors are not allowed inside these cars but can take tours of other cars. This first set of pictures is from the saloon
Was the fare royalty paid fair? Probably not as many extra railroad personnel would be added along the route to ensure the car's safety. Victoria started her 64-year rule in 1837 -- about when railroads began hitting their stride. When Queen Victoria traveled, a pilot engine would proceed her train by a 1/4 mile to ensure no hazards lie in front of her train. No other trains were allowed after hers for fifteen minutes. Similar precautions are still taken today with royalty. (Their present cars were put in service in 1977). That Princess would not have died on a British train.
Apparently the Queen did not have to use plastic forks and paper plates. She probably got to have liquids in her carry-ons as well. (I'm sure someone else would do the carrying on).
This last picture is of a much older car. (The ones above, I believe, were used during WWII). This may be of Queen Victoria's saloon -- what they called her visiting area. They obviously derived that word from the French salon, not the American west vernacular. Not a spittoon in sight here.