Be aware that your cheap more than motor insurance may include an excess payment in the event of a claim. The excess is the sum of money you need to pay in the event of a claim on your policy. This amount can vary from company to company and quote to quote.
If you've had an accident don't get any repair work done until you have cleared it with your car insurance company first. It is possible to choose a car insurance company who have agreed car repairers, to save you driving around getting quotes. They normally gaurantee their work also.
A lot of car insurance companies are now looking at customer's credit ratings, so if you have a good credit score you may benefit from lower premiums.