The simple answer is yes. The general rule is that the owner of the premises will be liable if he or she was negligent. Thus, if a slate falls off your roof and hits your neighbour's car and you knew the slate was loose, or you had not inspected the roof for a long time, then you would be deemed to be liable. On the other hand, if the falling slate was the result of an unusually fierce storm you may not be liable as it may be argued that you were not negligent. The same rules apply if a tenant has a flat and is injured by something falling from the landlord's part of the building.
Complications arise if the accident involves someone who is visiting the house.
While the general rule is that the occupier is liable if he or she was negligent, the rule has to be modified to deal with uninvited guests such as burglars, squatters and other trespassers. It would be unfair to make the occupier liable to these trespassers and so the law provides that the occupier is not liable even if there was negligence. For instance, if burglars trip over an uneven step they cannot sue the householder. In addition, children cannot be expected to stay off private property. Since children are naturally adventurous and curious the householder must take precautions to prevent children from entering dangerous property.