Loose cables across my property

Firstly, i am not a virgin media customer, which might explain Virgin's total lack of action in this regard, despite raising numerous complaints.

When i purchased my property, there was a legacy virgin broadband connection - this was a loose cable which originates from the pavement and trails across the driveway and up to the wall.  To complicate matters further, the same cable is used by the adjacent property, yet runs across my driveway.

Firstly, is it standard practice for a broadband installer to run cable across a surface, rather than sinking the cables underground?  

Secondly, and most importantly, the cables are a significant health and safety hazard - i have tripped over them numerous times, not to mention guests.  Presumably Virgin would be liable if someone was seriously injured?

Does anyone have any advice in getting Virgins attention to resolve this - a Virgin rep suggested i just cut the cables, however i understand other properties share a live connection using these wires...