We're with Direct Line and have claimed for various things over the years. We have found the cover to be good and their attitude when dealing with the claims was good too.
However, we have queried the premium each year for the last 2 or 3 years and each time we got a substantial reduction. They said that they used some sort of multiplier to do with our postcode to produce the premium that they automatically send out, but are able to adjust when when they look at your individual property.
So, as well as looking at comparison websites and/or checking with a broker and/or chekcking with companies directly, I'd definitely give Saga a call and ask them what they can do for you. (Assuming you were happy with Saga's service.)
Good luck.