The only problem with shopping around for better deals is that some of the 'better deals' are harder to get money out of when it comes to crunch time. (No pun intended) Not a big problem if you're in the wrong and the person you hit is chasing them, but a big pain when you need to claim. I went through this recently with some property insurance that I got through my bank from a major insurer. When I went to make a small claim, they were going to penalise me by putting my premiums through the roof, it was cheaper for me not to claim. So I switched to QBE, costs me maybe a couple of hundred extra each year, but I have never had a problem with payouts from that company and have never been penalised for claims.
Watch for little loopholes as well. I had a bike insured once, for the first two years it was 'new for old' replacement. That was what got me in, after the two years my insurance form said $7,000 or market value. So checked what the market value was and it was around $5,500. So I was paying a premium on seven thousand to get a payout out on five and a half.