Relax! The insurance problem which could have resulted in grounding the fleets has been resolved for the time being. Plus, any company which operates near a potential war zone will adjust its routings to avoid it.
Its no good getting in a stew about all this. All British aircraft will be insured as Airforce has said. Unfortunately, you nor I can sort this sorry mess out, what ever we do. What is going to happen will. Remember that what you hear and see in the news is what a reporters view is and the best way to sell news is finding bad news however small and then developing it.
Go to work, do your job and keep smiling (at least in front of SLF). Sadly and ironically, there's probably no safer time to fly with the airlines than now.