It might perhaps be Tyrolean or some attempt at a primitive effect.
Anyway, it looks like a lime mortar render. It may have been worsened by an impervious paint or coating.
I previously had a house of similar age, with a similar, but more pebbly, render. Lots of the pebbles had fallen out, and the lime was perished, cracked and scabby.
Best to have it hacked off and replaced with whatever suits your taste. Lime comes off fairly easily and you might find the house looks better without it. Sometimes render is applied to hide damaged or shoddy brickwork, so get it off before you decide what to do. There might also be water damage, e.g. from gutters, bays or downpipes, or a porch roof.
The windows suggest it was expensively built. Hopefully the general quality.
Painting exterior walls is a bad step, because if you do it once, you have to do it forever.
