You dont state what kind of trailer this is, i.e. small, large, commercial?..... however, if you park a trailer on a public highway there is no requirement for taxation, and no it does not have to be attached to a vehicle. What you must take into consideration is that if anyone in another vehicle was to collide with it they could claim it was parked dangerously which could cost you in the very least a Fixed Penalty Notice for dangerous parking, so make sure there is some kind of lights around the trailer. Also, if it is an HGV type 40 foot long trailer these have to have a test and plating certificate fastened on to the trailer, if it does not the re are numerous offences involved, again it should be lit at night