So, update...
BBC Radio 4's "You and Yours" (a consumer affairs programme which has apparently been going since 1970!) is featuring this Axa "issue" on their show on Thursday 5th Sept (it's on between 12 and 1pm just after the news). I spoke with them earlier (went into the studios behind Broadcasting House and sat in an empty studio while being interviewed remotely) and they're interviewing another person who's had a 470% increase, and had asked Axa to comment (no word yet).
The story will also be featured in Dog's Today magazine at some point!
Have also sent off a complaint letter to Axa.
We shall see what happens! Shall keep you all posted.
In the meantime, need to take out a new policy (assuming I lose this appeal) - probably with PetPlan.