The current company wont refuse to insure him. All they can do is to put the premium up. Usually they do this if there has been any claim within the last three years. Maybe there is something about the car your dh is not telling you?
I had an accident where a skip hire truck swerved and overtook me in the inside lane. The skip drivers version was that I had hit him from behind, whereas I could see what he did, as he rammed me on the drivers side as he swerved out. The cost of repairs were astronomical, and we had a courtesy car for 2 weeks, as it fractured the engine.
As he lied about what happened (possibly because he did not look in the mirror as he swerved and could therefore not see me, he might not have seen what happened) and his insurance company did not believe me, it went to the lawyers, and they decided we had to share the blame. I had protected my no claims bonus, but the insurance company decided that I was to blame, and the put a "note" in my records. I wanted to insure with a different company when my insurance was up, but couldnt as nobody would insure me. This "note" had been distributed to all insurance companies, so nobody would insure me. But, as they were my current insurers, they were by law obliged to keep insuring me. (In addition to this, our window had been smashed by a "maraudering teenager", and I had a very intimate encounter with a column in Sainsbos carpark. This three incidents within a 5 year period was enought to make a "note" on my account.)
Your dh has to call his current insurance company and sort it out.
sorry about writing such a long essay