If you notified them that you did not wish to have it stored and you filed your claim with your insurer, then you should do two things, one of which you already did (notify the towing company that you specifically told them you did not want it stored) and second you should notify your insurer and send them a copy of the bill and ask them to deal with it if you had comprehensive insurahce.
You may have an argument if you told them where to tow it, you cannot just tell them you do not want it stored and then give them no instructions as to what to do with the car. If once you filed all of the paperwork, you notified them where to dispose of it, then you could argue you are not liable. If you told them to tow it to your home, then you are not liable, but if you did not give them any instructions on what to do with the car, you may be liable to pay the bill.
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