I'm lucky I think that all the animals here are with a different insurer to Axa - in future I'll be making sure I don't take out any policy with them even it if means paying a bit more for house/car/life etc I'm not sure I'd want to trust them with any sort of policy if this is how they conduct their business.
I'm really sorry that has happened to you it's a huge amount of money to have to pay 
I checked my house policy to make sure it wasn't with Axa. I never want to deal with that company ever again after this! Talk about losing customers' trust! I will tell everyone I know to boycott them too!!
FYI - just read this on the website for the ABI (Association of British Insurers, I think):
"The FOS [Financial Ombudsman Service] will take a complaint further only if you have already made a formal complaint to your insurer and received their reponse. The FOS does not take on cases that are outside of its jurisdiction, for example it will not take on a customer complaint about premium increases being too high." - appears to be outside of the Ombudsman's jurisdiction. There is a Code of Conduct, which I'm investigating at the moment! Putting premiums up 600-1000% must be outside of some kind of code of ethics!
