Hi Gavin and welcome to the forum.
You maximum towing capacity is the 'actual' weight of the van. Tare weight is the van as it leaves the factory with no contents. ATM is the maximum weight including the contents. Thus the vehicle will be actually towing anywhere between the Tare and the ATM (legally), depending what you have put in the van. If looking at a vehicle which has a maximum limit of say 2000kg, then that is Tare plus contents.
In that context, you could have the scenario of where a vehicle is rated at 2000kg, the Tare of the van at 1700kg, the ATM of the van at 2100kg (more than the towing vehicle) and still be legal. However, the payload in the van could not exceed 300kg, as this would then take the 'actual' tow weigh to 2000kg which is the vehicle limit.
In terms of insurance, if a vehicles and van exceed their limits, they are not legally allowed to be on a public thoroughfare.
If involved in an accident, and the vehicle was not legal to be driven in the first place, then yes the insurance can be made void. It is irrespective of whether it was a contributing influence or not, just whether it was allowed to be there or not. This is the same as to if a car was registered or not. It may be safe to drive and its registration had no bearing on the accident, but if it wasn't legal, insurance won't touch them. You refer to the Insurance Contracts Act, which yes does refer to "Where the insured proves that some part of the loss that gave rise to the claim was not caused by the act, the insurer may not refuse to pay the claim, so far as it concerns that part of the loss, by reason only of the act." However, in taking out the insurance we agree to abide by the Terms and Conditions of the Policy which I'm sure will say somewhere that we need to be road legal.....if we could be bothered reading it

AAMi did advise at one point if only slightly over, they won't care. if about 10% over, it will be questioned, and if 20% over, no hope.
Andrew
edit: From AAMI website:
Am I covered if? If your caravan was loaded above the legal limit or loaded in an illegal way. NO
from CIL
We may refuse to pay a claim under this policy if:
- your caravan has been converted or modified by someone other than the manufacturer and these conversion or modification details are not shown in your schedule.
- your caravan is being towed while it is unregistered, or the towing vehicle is unregistered.
- your caravan is being towed contrary to any law.
- your caravan, or the way it is loaded, interferes with the proper control of the vehicle towing it or your caravan.
Lastly, at best, legal action may result in the insurer paying out on damages to the van even if overloaded, but I'd be pretty confident if something happened to another person, your Personal Liability insurance would be harder to get resolved....
Sorry to harp on, but I've been having to research this a bit myself lately since my ball weight is over limits...