The problem is I don't think that London really does divide into four neat quarters, in terms of allegiances, historical links, or continuing culture!
Partly there is the urban/suburban divide (is Erith really SE London in the same way that Battersea is SW London?), partly there is the continuing legacy, in some, but not places,. of the pre-1965 (in some cases, pre-1889) boundaries - Essex-in-London, Kent-in-London, Middlesex and in some areas Surrey-in-London still live on... (in the latter case the radically different political allegiances. when compared with the rest of Greater London, of the boroughs of Kingston and Sutton and Richmond highlight their non-London nature and origins....wheresa Croydon nevermind other former territories of Surrey have by now been thoroughly assimilated to London norms)
The N/NW postcode split makes sense to me too: the NW postcodes are mostly a fairly cohesive and distinct set of areas that don't look to the same places as most of the N postcodes. And Uxbridge is patently in no meaningful sense other than the pedantically administatively "North-west London") (Should the S postcode be taken back from Sheffield to form a coherent central chunk of London maybe centred around the Morden Branch of the Northern Line? Perhaps. Although Hackney balances on a boundary carefully, I'm not convinced NE is needed in the capital again though).
In the East, the Rivers Lea and Roding serve important boundaries - gradiations of eastness/Essexness, maybe. But clearly East London spreads on both sides of probably both of those rivers now. (Is Ilford meaningfully in Essex any more? Less so than even 20 years ago. Romford, though?)
I think my boundaries, however ill-defined and uncertain, would divide the city into not four chunks but rather nine@
1. Continuity Middlesex (focal points Heathrow, Hayes, Uxbridge, Harrow, Enfield) (This forms an L-shape running almost the entire height of the western boundary of present-day Greater London, and also sweeping East along the northern borders as far as Enfield, probably inevitably annexing a bit of historic Herts on the way)
The other territories are more or less arranged in belts running west to east:
The northernmost belt
2. NW London (focal points Edgware, Finchley, Golders Green, Hampstead, Kilburn, Camden)
3. N London (focal points Tottenham, Archway, Holloway, Wood Green)
4. E London (everywhere East of the Lea, including Essex-in-London, plus Hackney & Tower Hamlets)
Central belt (central area only)
5. Central London (essentially inside the Circle Line and a few bits outside south of the river)
The southermost belt
6. Surrey-in-London (the boroughs of Kingston and Sutton, and some of Richmond south of the river)
7. SW London (focal points Wandsworth, Wimbledon, Battersea, Clapham)
8. S London (focal points Brixton, Norwood, Croydon, Lewisham)
9. SE London (focal points Greenwich, Woolwich, Bromley, Bexley)
I wonder if rivers could be used in part to define the boundaries between SW and S, and S and SE. The Wandle, or Ravensbourne perhaps?
