I always fall off my seat whenever the car insurance renewal comes through. Virtually every company I've ever been with claim that, despite tirelessly searching for the best deal on renewal, have ended up upping the premium by 50%+ (despite yet another years no claims).
I always use the comparison sites, get a comparable quote elsewhere (also worth checking reviews of the companies you're looking at, as cheap isn't always better) and see if you're current insurer will match. If they don't, then swap. No reward for loyalty in the car insurance game. Just the opposite, in fact.