@Charlotte311 I hope you have also contacted your own insurer. I believe the liability part of Aircover is a proper insurance policy so if you have anything like the UK Insurance ombudsman you should be able to refer Airbnb to them if you do not get a proper service.
@Charlotte311 An injury from what? Just because a guest was injured on your property doesn't mean that you're responsible. It depends on the circumstances. What are they saying happened?