I guess it depends entirely on if that "layby" is in the deeds of the house, or is part of the highway.
If the former then it's technically their "driveway".
I'd be surprised if anything like that parking area would be in the deeds of the property.
By the looks of the picture it doesn't look like it's a dedicated space, more of a "first come first served" basis.
Guess the OP can only report and wait for someone to come along and decide if it should be towed.