I can only give my experience which is from cable laid many years ago.
The grey cabinet is a few yards from my house on the opposite side of the road, they do not use an overhead cable to cross the road. Any underground work has long been covered over with new pavement/tarmac but must exist as I watched the engineer walk over and work in the cabinet when they connected me.
Along our street the cable access is a small plastic tube that is set flush with the ground outside each property, covered by a black cap. Our drive is gravel, but there is a border of shrubs and flowers, they ran the cable along this but didn't bother burying it (I suspect they should have), but it does mean I can see it runs inside a plastic tube for protection, so I don't see why they couldn't run it along a wall to your property.