Theoretically you should not need to inform your insurer about changing from run flats to regular tyres as long as you change all four at the same time and they match the original specification in all other aspects. However, we have seen reports that some insurers do require you to inform them of this change and that your policy may be invalidated in the event of a claim, so we would suggest contacting your insurer to clarify. We would not expect this to affect the cost, other than a potential charge for a change to your policy.