Simply write to the Insurance Company and provide the details - do not refer to it as a 'mistake' - it is not a mistake if they have asked you. An Insurance Company is not permitted to invalidate a claim for an issue such as this.
I worked in Claims and Underwriting for a well known Motor Insurer for 20 years. When an issue of non disclosure arose we asked Did we ask the question at the proposal stage - did they lie?. Even if there was a lie, would we have insured them anyway on the real details? I f yes, the client had to pay the extra premium if any. If no, we may have invalidated the claim for damage to the policyholders car but we would have been liable for any damage or injury to the third party. This is not an option for an Insurer it is the Law - UK and European Directives apply.
This is not the situation for you - it is a non fault accident. The other side have no right to ask you these questions with a view to invalidating a claim only for clarification of who to make the offer / pay the cheque. Tell your Insurance Company about the ownership as it has been brought to your attention. Any 'member of the public' has clear protections with regard to Insurance Proposals - if the Ins Company do not ask the question they do not have an automatic right to the answer. There are many cases (Legal and under the Ins Ombudsman) that rule that a member of the public cannot have the knowledge of an Insurance Underwriter and will not know what is material, important or bound to be disclosed. If they ask the question you have to answer it truthfully to the best of your knowledge - if not, you cannot be held responsible for any omissions.
It is not a problem to purchase or own a car for your mother, sister, wife, brother etc it is only a problem if you are trying to conceal its real use. e.g you own it and you are 17 and you insure it in your dads name and say he is the main driver when you are, otherwise if you own it and your wife and mother use it no problem!!!!