I'm on my 4th trailer for my Caterham. The first was an 8 x 18 open all aluminum H&H tilt bed trailer. I towed it with a 2005 Subaru Legacy GT and got around 20 mpg.
I got the above mentioned paranoia about having the Caterham exposed overnight in motel parking lots and bought a home built enclosed trailer from an SCCA racer. It was horrible towing, swaying all over the place and very inconvenient to use. I towed it with a 2005 Silverado 1500.
The next trailer was an 8 x 16 full height, flat front enclosed trailer by United Trailer. It towed well but I got only 7 mpg at highway speeds. It was also towed with the Silverado.
The current trailer is a 7 x 14 Haulmark LoHauler motorcycle trailer. It has a V nose and you cannot stand up straight in it. Gas mileage went up to 11 mpg with the Silverado. I traded in the Silverado on a 2011 Ram 1500 and gas mileage went to 12 mpg and I can exceed the speed limit going over Vail Pass (10,600') and the run up to the Eisenhower tunnel (11,XXX') on the cruise control. Even if I get slowed down by traffic it can recover back to speed.
This trailer is perfect for what I haul. The Caterham fits nicely with room behind it for the 10 - 10' canopy and room in the V-nose for tires and tools. I can even get a Miata in it but have lower the top and climb over the doors to get in and out of it. Both pickups have a topper over the bed and anything that doesn't fit in the trailer goes in the bed. It is the best towing trailer I've owned or borrowed. Never sways at all and I don't have the special antisway bars or equalizer hitch. I've towed it to both coasts and up into Canada and many trips over the Rockies.
The Ram pickup has the towing package with mirrors that rotate from horizontal to vertical for towing although I prefer to tow with them in the normal position.