Having street lights is not the only marker of a street being a built up area.
My understanding following my speed awareness course is that the NSL sign (black diagonal) does indicate the National Speed Limit which is 60mph for cars. In a built up area the National Speed Limit drops to 30mph BUT there should be a 30 mph sign to denote this zone i.e. number 30 inside a red ring.
The reason you need a speed limit sign in a reduced NSL zone is to avoid the type of ambiguity and confusion that is reigning on this thread. Again, some roads that are not in built up areas may have street lights and visa versa.
At the end of the day the signs rule. You are only told about the street light thing on the speed awareness course to make you aware of certain visual cue’s to help you see in advance when a speed limit change is coming so you can look ahead and make better decisions. But ultimately the signs rule and a black diagonal sign means 60mph for a car. Other wise why would you need any other speed sign at all? All signs would just be the black diagonal and leave it upto drivers to decide what the speed limit was based upon there being street lights or not.