FD, thanks for that (first) post clearing things up.
In that case, I take back what I said about things being different on the left side of the ocean, as really, by reading the last 2 or 3 posts, it boils down to the same thing!
In laymen's terms...you can't continue past the OM or equivalent, unless you have required visibility/RVR (for the type of approach you are conducting). And if vis goes down below req'd mins, once inside the OM/FAF, you can continue to DH/MDA "and have a look"!!
Continuing to land only if you have all the other stuff BOAC mentioned, otherwise MAP.
Correct me if I'm wrong, but over here (Euro/JARland) you also must have the minimum ceiling, whereas in the US only visibility is a controlling factor on whether you can start an approach or not (precision or non).