Ignoring Jean's event in this - I expect it was organised as 'friends' attending a private function. The issue has become that to show a car at most events you are required to have insurance. This is in addition to the organisers public liability insurance as they often cannot/will not be responsible for an attendee doing something reckless with his own machine. This would be sued as negligence by the exhibitor's insurer and hence the need for insurance by each exhibitor. Now most of us are sensible and a rather sad Frisky on a trailer parked is a danger to no one and John is unlikely to be the sort of person to decide to fit a wrong engine and proceed to drive around until it catches fire or something. Nonetheless organisers can and will insist on insurance on the 'what if' ticket. What if two kids got in the Frisky and set it alight. Common sense says they deserve to get burned with the car for being stupid but sadly the law no longer works that way. Pratts have the right to be stupid and destroy your property and sue for getting hurt in the process. All part of the general abdication of responsibility for self promoted by 'socialism' etc.
Secondly not many people have proper insurance cover for a trailer. Most policies will cover a legally towed trailer. Some el cheapo quotes do not even do that! The most policies have a nasty caveat though. If the trailer and/or load become detached from the tow vehicle it is not covered by the policy. Therefore theft, broken hitch, load off from failed straps - no cover and that includes the damage done when it hits Alan Sugar's Roller coming the other way! This in the same way that if you get hit by a guy who died at the wheel of his car will result in his insurers not paying out as the policy ceased when the driver died. So the policy cover ends as soon as the link with the insured car is broken. Further many of the Campervans that folk insist on taking to events are probably of illegal weights and therefore by default the trailer will be uninsured or being driven be a driver with the wrong license or even equipment in the cab - a big camper with large trailer would be requiring a tacho! So your car popped on a trailer is potentially at greater risk than many think. Dumping a dead car on a field on or off a trailer does not offer any insurance as several people have attempted to tell me unless you policy specifically says so. A frames, do not get me started, lets just say they are not as good an idea as they seem. Indeed the best answer to all this is to put the car inside the support vehicle, which is what I used to do.
Clearly insuring a vehicle that is not registered on DVLA is a bit more difficult that one that is. Insurers prefer an easy to define risk. The more complex, the more work and the more chance you forget an element of risk that will see the insurer wriggle out of a claim as it is upon you to advise the insurer of the risk they are covering and if that risk changes. This is why all mods and any law judgements served against you should be reported to your insurer. If you play cute it might just cost you. I can suggest several examples of folk who have had their lives devastated through a failed insurance policy. Our dear colleagues the Hallam's for instance. Hence the lack of piles of rotting trash at many shows these days, you know, the stuff we all like looking at. Microcar events have been great at holding back this reality and we still have tired cars bought to the national etc but it is probably not really a good idea if one buys into modern lifestyle. More so as more people seem happy to own running unregistered or unroadworthy vehicles which they will run around the rally area quite happily without insurance. See guy who decided to drive my KR175 around Brooklands without permission because my insured chum had a go and drove into Bob Cotton's Bond. Who pays for that? See unregistered Tri Tech rolling in front of groundsman at Kingham School. A venue lost for a non-Schmitter being a pratt.
SORN is a Government revenue collector introduced to control cars more tightly as the Government refuse to run a system which proves ownership with all the benefits that would offer for the responsibility of carrying accurate records. They know they cannot carry accurate records economically thus the fudge. The council system was far better but did not suit the control of the public nationally. The whole system is reven by the fact, what is a car? No actual definition is on offer so there are huge cracks in legislation. Is an unregistered car in three parts exported as a car, mechanical parts, art etc etc. A mess of Government making as responsibility and accurate law and records cost whereas having unhelpful spot bots threatening people makes free money without the responsibility of a simple set of rules. However an A framed car, as I understand it, needs to carry a valid tax disc as all its wheels are on the road. A dolly does not require a tax disc or insurance but is really an emergency device for the trade thus the drivers insurance is different. Neither option are permitted abroad in general as they apply their laws with more force, not least as they fine on the spot, unless your paperwork etc is in order. I have both dollied and framed across Europe using trade privilege I now no longer have, but pulling the limits of law as they are really for local 'get you off the road' work not international trade!
We all take risks on insurance and legality of transport but I think you will find the above correct. I will be pleased to be proven wrong as I can learn something.