You should discuss how the excess works with your salesperson or insurer. The insurer's annual review will take account of the costs of all claims paid by the insurer for its customers. Your premium will not normally be directly affected by your own claims. The no claims discount option offered by some insurers can help limit the increase of your premium. Premium rises are usually above the rate of inflation as explained below.
Healthcare costs throughout the western world rise faster than general inflation.
In the UK this is true for the National Health Service and the private sector, both of which see a steady rise in the number of patients being treated. As far as the private sector is concerned, improvements in technology expand the range of available treatments under most policies. As a result charges made by specialists and hospitals tend to rise above retail price inflation. In addition to a yearly adjustment for inflation, premiums will increase as you get older. Insurers vary in the extent and frequency of age increases.