Ideally, drivers who have not made a claim for several years (or decades) should be paying a very low sum for their insurance, as they are clearly less of a risk for insurers than someone who has been involved in several accidents. However, the reality is sometimes more complex.
For each year that you drive without making a claim, your insurer will award one year no claim bonus (NCB). Certainly, the first five years of building up an NCB are beneficial, as after that costs will generally start to fall rapidly.
After a certain period of driving (such as five years) a driver can pay to protect their NCB, so that the discount endures even if they have an accident. However, the way a discount is applied varies between insurers. Most allow you to make one claim in a year, or two claims in three years, and still keep your NCB. At the end of each year make sure you keep your proof of NCB, so you can use it for renewal.