Different insurers have different dislikes. Clearly drivers with any history of drink driving, driving without insurance and dangerous driving are going to have a difficult time. Accidents where only the proposer’s car is involved, especially late at night, raise questions and if you live in many metropolitan areas the incidence of damage, accidental or deliberate, especially if the car is un-garaged is magnified.
Insurers do not like being told after the event that something has happened. If, for example, you need to increase your mileage or add another driver, talk to your broker first. Do not expose yourself to the possibility of non-disclosure. In extreme cases the insurer could decline your claim. If in doubt, ask.