I’m not sure you’ll find much info relating to old parcel numbers. If you’ve found the walls in the context of a development I’d imagine you’ll have to follow planning rules/hire archaeological consultancy etc? They will do investigations accordingly.
Land ownership is difficult but there’s things like local knowledge, land terriers, if it’s public land there’s probably more chance you’ll be able to find the owner easily, there’s currently a big push on registering public land.
There’s the historic England/Scotland online maps too to see if it’s something scheduled, which is unlikely if it’s just old walls.