It's not a straightforward issue, but this looks to be a fairly authoritative source - for the UK at least.
http://www.ttas.co.uk/towsafe.cartransport.html
That is what I understand to be the law too. It changed toward the end of the 90's I think. Before then towing dollys were fine and I used one all over Europe, though the rules varied. I had to talk myself out of a few situations but clearly the situation was confused.
There are hidden risks in using dollys too. The law states the assembly is considered a trailer. So despite your expensive classic insurance guess what your insurer will say if you have an accident with your expensive classic car on a dolly. This would remain the case if your home made dolly failed and parted from the tow car, it is still a trailer. SOME NORMAL GENERAL INSURANCE POLICIES COVER TOWING, MOST DO NOT COVER TRAILERS 'UNATTACHED FROM THE TOW VEHICLE'. It pays to check but a failure of an articulated trailer is a guaranteed accident to the car towed and it could be neither insurance on either car will pick up the bill. A piccy copper could seize your 'trailer' as it is not insured or safe.
Some cars are not suitable for towing anyway. See where the drive train is turning the engine, travelling in reverse and not sending oil round the drive train which is design for Oil dispersion forwards. You still wear out your consumables like tyres, bushings etc. Neither is the tow car design for speeds in excess of the original performance window. Variomatics are simply not to be towed save in an emergency due to the drive management system and risk of perminant and expensive damage.
For all these reasons I dispensed with the Dolly in favour for a van or trailer. It is simpler and safer. The only real advantage of a dolly was always its ease of storage, light return tow weight saving fuel and convenience of use when moving other peoples machines or cars not being as I was not paying the maintenance costs. I retain an A frame for Isetta, Trienkel and 'Schmitt as they can be very handy for delivery/collection including ferries and tunnels where saving on fees can be obtained.
For the above reasons I now 'over trail' by using a light weight ex racing car four wheeled trailer even on small trikes. If I moving a £15k Messerschmitt I do not want a puncture pulling the trailer into an accident. Been there, done that. The unused area round the car on the deck gives space for intrusion of other things not to reach the car also. So I can mow down cyclists without risking damage to my well placed Schmitt, for instance. Important when you live near Oxford! Yet the light weight keeps fuel use down but for the drag of the extra axle. The down side is it needs a 15ft by 6ft parking space. If I were stuck for space I would fit it with several curved rails and mount a winch on the wall so I could pull it onto its side for when it was out of use. My box trailer lives on it tail against the wall for this reason having been made for this option. Indeed it is also a great anti theft device and could be padlocked in place.
