I have owned a couple of Land Rovers and used them to tow trailers. Not my Airstream as of yet since I am in the process of restoring it. 1968
However, I have towed a 1960
Ford Thunderbird and a 1955
Land Rover Series I 107 pickup on a 24 foot car trailer. The trailer did not have brakes. I have towed with both a Series I and II Discovery. Both vehicles handled the weight with no issues and was able to stop the trailer with out problems. Granted these were properly loaded trailers. The Rover 4.0 V8 is a bit under powered, but it is still has good torque. It does the job, just slowly. I also have Old Man Emu heavy duty springs which help with the weight.
The articles that are linked are regarding the LR3 which has a different hitch design. In the UK they have better hitch available that does get securely bolted the chassis and not just use the quick release system that we have in the states.
I am looking at picking up a truck my family owned when I was younger to be my Airstream tow vehicle... a 1975 Ford Crew Cab 4x4. It will get a rebuild with a newer 5 speed, fuel injection etc... however.