Yes, I think you must be right on both counts - cement-based and lime-based respectively. Once one is below the surface (which is smooth, and seems 'hard'), the latter really does both look and behave just like 'sand', and some of it contains (I suspect horse) hair. The hard one is extremely hard, far more so than, say, brick-laying mortar, and is at least as hard as render - a mere 'hammer drill' struggles to get through it, one really needs an SDS one. It also can be anything up to a couple of inches deep, most commonly about one inch.It sounds interesting John. Have you any idea what the type of plaster might be that's the "hard one" - would it be some type of cement based rendering product? Would the plaster that looks similar to "sand" be lime based?
The strange thing is there doesn't seem to be any particular pattern as to where in the house the two different types exist - they both seem to exist in both the Georgian and Victorian parts of the house.
Kind Regards, John