The council could argue the burst pipe leaking water was the cause of the subsidence and/or caused the tree roots to grow more in that direction than they could have expected, so therefore they are not liable.
As I said before, all sounds very messy.
I would be inclined to speak to the insurance company and basically ask them to put in writing that you will not have to pay a single penny if they go ahead and lose, because it could be some free money, otherwise walk away.