Insurance is centre-square on this topic. No-one likes to drive uninsured and the potential consequences are appalling.
I find responsibility dodging by UK insurers is very tiring, especially when there is specific European insurance legislation which covers the situation and aims to protect the consumer (that's you Martin), not the big, fat corporation.
Reassuringly and very interestingly if you go to the 'Ring you'll hear a very different story to that which Martin the insurance salesman is trying to tell. This is from the UK people who live out there, who talk to those UK people who are unfortunate, or stupid enough to bin their car and then have to claim on their third party insurance. Why? Because it's not possible for underwriters to slime around European legislation.
The 'Ring is a road, not a racetrack. Look it says here:

For those struggling to read (or if the image isn't up) the barrier says 'German traffic law is valid. Keep to right lane.'
You wouldn't know about that sign, Martin as you've told us you've not been out there.
Why does the barrier say this? Because it's a public road, not a racetrack. The driving I've done out there is called 'TouristenFahrten' - Tourist Driving. I don't time myself and I'm racing no-one. I'm driving one of the most stunning roads in Europe purely for pleasure, which my insurance covers me to do.
So your general insurance will cover you third party, unless you ask your provider and have been specifically recorded as being told that no, you're not covered - then you're into a dodgy situation if they say no (which is the automatic knee-jerk response).
Sure HIC offers insurance from some large underwriters who have been busy writing dodgy clauses into their policy documents, but there is still a goodly spread of insurance underwriters who haven't tried to bolt their policies down in illicit ways to stop delivering consumers their legally enshrined European minimum rights.
Did you actually ask your new insurers specifically if they do cover it? Anyway, the moral of the story, always check with your insurers if they cover it.
Why would I? That would be a really dumb question. I didn't ask if I was covered on any other high risk roads like Route Napoleon in France, or the Stelvio Pass. I did ask for clarification as to whether I would be covered on the roads where the Le Mans 24hr race is held (I've been for the past couple of years - a top quality event). You see, sometimes those roads are used as a racetrack and there was an exclusion pertaining to that in my policy that I was concerned about. I was told provided the road was being used as a road, not a racetrack then OF COURSE I was covered (well DUH!). It's good that all these conversations are recorded, as what's good for the goose is good for the gander.
The biggest problem is that some UK insurers don't seem to understand European law and some UK underwriters don't understand what the 'Ring is.
I would LOVE to do it myself!
Well Martin, the good thing is that you CAN do it. I think the biggest problem is that you're with the wrong insurer. I know of a number of UK insurers who will cover you on the 'Ring and make it possible for you to go out there and drive it completely legally. You can always get in contact with me if you need some help finding good (not just cheap) insurance cover.
In other news muppets showing up with German-look plates are generally turned away at the barriers. Yet another reason not to buy chav-plates.