Tom,
Insurance underwriting is essentially the assessment of risk and the lower the risk factor, the better it is for insurance companies and the less you will pay in premiums. Drink driving is both a serious and dangerous offence. Not only drink drivers are a threat to themselves but to others as well. If involved in an accident, life could be at stake and damage could be done to the vehicle or public/private property. If for whatever reason your claim is rejected by your car insurance company, this does not necessarily mean that they will not spend any money regarding that claim. Money is lost in processing your claim (even though the outcome for you might not be pleasant), compensation may have to be paid to third parties and fees are applicable in disputing the liability for your claim (proving your claim is invalid). That is why your premiums will go up if you already have a drink drive conviction because the risk of you committing another offence is higher than somebody with no previous convictions.