There is a direct relationship between your claim and insurance premium going up. A chargeable claim is one that the insurer considers to be your fault. It is spot on your record as you will be continuously charged this increase long after you have filed the claim. Even if you make too many claims company may decide not to renew your policy.
Most importantly filing claims are not the only way to see your premium go up. Marks against your record can also increase your premium. Certainly if you are found with drunken driving conviction they result in a large premium increase.