As far as I understand it, in this context, the meaning in BrE is the same as that given by SoothingDave.
"North" when used as an adjective tends to relate to whole items: eg. countries, states, counties or even well defined areas with proper boundaries within a county. e.g. North Somerset (in the red boundary)
http://tinyurl.com/pktt94d , North Yorkshire (in the red boundary)
http://tinyurl.com/obfpl3u , or even North America
http://tinyurl.com/ofd2v93 (the whole continent).
"Northern" tends to refer to part of something else; a region, or a more vague area, where the boundaries might not be so clear cut and may have changed much over time. e.g. "Northern Ireland" - the part of Ireland in the north, "Northern Europe" - the vague part of Europe in the north [vague because where does south actually end and north begin?] and "Northern hemisphere" the north half of the globe.
As Matthew pointed out "North London" is a name for a defined area of the city including specific London boroughs. However, the confusion arises because you can quite legitimately talk about "northern London", to mean a more general concept of everywhere in London north of the Thames.
So going back to your sentences:
North London is OK. [A specific area of London].
Northern London is OK. [A more vague area of London covering anywhere north of the Thames].
North France - Doesn't work. [Because to my knowledge there isn't a specifically defined region known as "North France"].
Northern France is OK, as this is just a relatively vague name for anywhere within the northern half of France. However, generally we tend to think of it as being the areas along the north coast.
