I am not sure that it's against the law to have an uninsured car. Yes, you need to be insured to actually drive it on the road, but providing it is taxed if on a public road, then that's all that matters. Providing you stay parked, you and it can do no damage, the only problem with it being uninsured is that you suffer any loss for damage to it.
I say that because there was a time when my car wasn't driveable and I wasn't sure if I was getting rid or not. It still had tax, but at the same time the insurance expired, and I didn't bother renewing until I knew what was happening.
One other thing, again some years ago I had to attend a week's training course 50 miles away, and a colleague also went. I actually got him temp insured as a named driver so one could drive down, and the other drive back. There were no problems with this at all.