How heavy is the trailer ?  : There are 2 seperate trailer classifications in Spain - each one different : Up to 750kg and over 750kg

You can tow trailers up to 31/2 tons on an english licence.
You can tow up to 750kg on any spanish licence above that you have to take a rest.
If you tow above 750kg with a spanish car you must have the spanish licence with the additional weight allowance or your insurance is invalud.
If you tow any trailer on a spanish reg car it must have a current plate (almost impossible to get on a uk manufactured trailer except ifor williams)
Obviously its easier to tow using an english reg car but then you are restricted by the 1 month 6 month rule for residents or foreign nationals.
Way round this is to use commercial vehicle ie transit, terrano commercial (any vehicle with fully enclosed rear).
as it is then considered restriction of freedom of trade across the EU if they impound you & therefor illeagal.
Hope that helps