Maybe if the cable companies paperwork doesn’t add up. If the cabinet is on private property then at some point a wayleave for its position and maintenance must have been granted by the properties owner. You need to see a copy of this to know what was aggreed. I think that unless a convenant was added to the title deeds of the property to allow the cabinet(which due to expense probably wasn’t) then the cable company probably needs to negotiate the wayleave terms with each subsequent owner ,so yes you probably could if this is the case charge rent or make them move it. The wayleave would prevent you building a shed around it—–no access

No.

When your parents bought the house, part of its title includes an easement for public utilities.