I would have thought the only problem is that of the driver's licence, but my own view is that if not done for hire and reward it's the same as using any other private motor car to tow, i.e. if I tow my mate's car with mine, so I extend this to the militant if I have to tow anything, as in essence it's a PLG, but has free tax and no mot on the basis of it's age, and non-commercial use.
If you were to come a cropper, it would be with your insurance company, and if they are happy that the tow is private, I think that is it. I know others will say different, but I've done this for years with no ill effect.
I don't see what benefit it would offer whether the vehicle is tested, insured as a wrecker for commercial use and the driver suitably licensed, given that you are not using the vehicle commercially?
I always consider that if the worse happens, will my insurance pay out? If so, then I must be on the right side. If anything, you might find that it is the vehicle being towed who's insurance is invalidated? As I queried recently whether I could tow a FH70 behind the militant, and was told that it would be covered for third party claims, but not for damge to it unless I sought extra cover.