Yes, the supermarket is liable if the use of their property causes a "tort feasor" to occur to yourself. I would suggest speaking to a solicitor, as it is outside the scope of what I normally advise on. Ultimately it is covered under the law of trespass, as they are causing financial loss to you (damage to your property) as a result of them allowing users of their property to move onto yours. This should mean they are "vicariously liable" for the actions of the people using their land should it damage yours.