@arg
So based on what you've said, I guess the problem would be if the voltage is consistently low while the car is charging at 32A as this could drag our entire property's supply voltage down to a point where there could be a danger of overheating cables attached to any high load anywhere in the house or garage especially if this were over a long period.
Does that sound that right?
I think you've slightly misunderstood here. Assuming everything is as you say, the risk is that the car thinks there could be overheating cables in the house when actually there are not. If nearly all of the voltage drop is in the supply wiring, then it's the supply wiring that might possibly overheat (which, so long as it's outside the house, could perversely be a good thing because they will be forced to fix it!)
How low a voltage is actually dangerous in this kind of situation?
Low voltage is in itself very rarely dangerous. (I was going to write "not" rather than "very rarely", but to be pedantically correct there are a few things that can actually overheat as a result of low voltage - primarily old-fashioned types of electric motor - but you are unlikely to have any of those in a modern household, and the degree of voltage drop we are talking about probably isn't enough to cause a real problem if you did).
What we are talking about is low voltage being a symptom of something else being wrong - if the voltage a moment ago was higher and it's now lower, where have those volts gone? If the voltage at the DNO transformer hasn't changed, then those volts have been lost somewhere between there and the car, and are turning into heat: if the voltage has dropped by 10% then 10% of the total power being delivered is now heat - that's a lot of heat! If the volts are being dropped uniformly along a very long cable from the transformer, then it's just a nuisance - that whole cable is getting a little bit warm as the heat is spread out. However, if most of the volts are being dropped across a poor connection between cables somewhere, then that's serious because all the heat is concentrated in one place and it will be getting very hot indeed.
Am I likely to have the same issue with any other electrician being cautious in this way? ie. are the installers being reasonable or are they just trying to walk away from a job that's causing them more hassle than they want?
It appears that your installers are inflexible - they have one fixed design that they want to use, and can't/won't consider any other. This is common in some organizations where they don't have sufficient fully qualified staff: the people doing the work may be good craftsmen capable of doing the actual installation work but are not qualified to do design. So they work to a number of fixed designs under the supervision of a qualified supervisor .
Regardless of this installation, I will be looking to stick an opensource current/voltage monitor and logging as close to the supply feed as possible so that I can go back to the DNO if neccessary, but the fact is that replacing the supply line to our house would seem to involve digging a trench across the neighbour's garden so this isn't really something I want to deal with if possible.
That does assume that the supply cable across the neighbour's garden is the sole source of the problem. That seems slightly unlikely unless it's faulty or you don't in fact have a 100A supply as you believe. (or it's an enormous garden, of course).