Whilst car insurance policies go up, because you're deemed to be a "less safe" driver once you've had a claim, my understanding is that home, contents, and landlord policies don't generally work the same way. eg If you've had a claim as a result of a storm, that doesn't mean that *you* are a riskier prospect than you were before the claim. We had a $250K claim on our home and contents insurance last year (after a flood) and our premiums - with the same insurer - went down about 20% this year. Premiums can go up if the whole city, for example, had a huge claim, and the whole city is perceived as riskier, but an individual policy holder can't be deemed to be risker for having been affected by a random event.
There are some specific types of claim which may cause their perception of your risk to rise, eg if you have a claim for a dog bite, they may deem your dog as a higher risk and your policy could rise, but a fire by a tenant would generally be viewed as "one of those things", IMHO, and I doubt your rates will rise.
Pedro61 has given me permission to post this, and I quote:
"FIY My insurance renewal came in the oter day and surprise ! The premium has increased. I called them to ask why and they said that it was because of this recent claim, and I had now lost my "No-claim bonus". So Mr Perp's claim that "I don't believe that previous claims affect the amount of your policy." is complete bollocks."
End quote.
So there you go folks.
You can just keep on having your premiums increase every year..and have nobody to blame but yourself.