Price comparison sites and reviews are the way to go.
With reviews, there is always someone who tries to claim for what they are not entitled to, and get very stroppy on reviews. So ignore those. If there are a lot of negative comments, be wary.
Some of the big names are as bad as the lesser known ones, and some of the lesser known names are just trading names for one of the bigger companies. When the name is big enough, they don't need to care about their reputation, as this is solid anyway. Churchill are still very popular despite being utter sh** bags to Bethany Probert's parents.
In any case, there is always the Insurance Ombudsman should you have any problems.
If you can't afford buildings and contents insurance, cancel all others (except your car), and go for these two. Unless you can afford to replace your house and everything in it in the event of fire, etc.