The artificial stone would appear to be what I knew as Bradstone or Fifestone. The rear looks like cast concrete. The stains are a mixture of soot, and accumulated dirt and dust. Sorry I can't be more specific than that.
GEEMAC, if as you said you have done the soapy water and elbow grease thing, I'd try to use brick acid can buy it at most DIY stores and builders merchants they may name it stone or patio cleaner etc , should contain hydrocloric acid. Try a diluted version at first to gauge the strengh needed so you only take dirt off and not surface of concrete.