I now have 3 cars (I know, I know) and change insurers each and every time. After another successful year avoiding hitting anything, the RAC rewarded me with another year's no claims bonus which helped my premium to go UP another 70 quid! A cheery letter advised me to "relax, you're covered for another year". Oh no I'm not, I rang them and told them there was no way they were to take the new premium of £286.24 - a few go compares later and I'm relaxed and insured elsewhere at £197.
There's not much loyalty in business these days - but in car insurance there is none at all - if you want to be loyal to your current insurer, you're the very customer they make their profits from.