I've found the following affect insurance prices:
1. Time owned the car (this is a BIG deal). I renewed my insurance on my Toyota, but I replaced it because the engine had gone on the older one, and the insurance DOUBLED just because on paper I had not owned the car very long (in reality I'd owned it for 2 years). This can make premiums shoot way off the scale! Try it and see, say you've owned the car 12 months.
2. No claims discount - This is just plain weird, and as seen above, you can get a better price for 2 years than you can for 3. How does that work exactly? Random number generator at work again..
3. Time since you passed your test. Age seems to be less relevant than time you have had your license. You can also try this on sites like confused.com.
4. Address. This one is plain stupid. I had a quote of £650 for my wife on her 182 at the old house (number 5). So I re-quoted with the correct house number and it went up to over £900!!! Everything else was identical. The car was even in a better parking space!
5. Points. This can really hurt you.
6. Excess. £500 excess can bring a policy down a few hundred quid, but usually makes claims incredibly expensive so best drive nicely!
These are all based on my fairly dreadful experience of dealing with insurance companies. To be fair on them, most of the people I have spoken to from insurance companies are as baffled as I am, especially with the 2 / 3 years no claims difference and the house number, and the time owned the car. There is no common sense tick box or manual tweaking, just all set by bean counters and faceless computer programs.
I'll get my coat..