Note that the area numbers W8 etc refer to the postal addresses - an
early delivery code or ZIP code system. It does not necessarily only
refer to post offices, although obviously all post offices are located
within these areas.Every premises postal address includes this code (
now including a supplement in the new nationwide postcode system. For
instance Baden-Powell House, The Scout HQ in London is SW7 5JS). There
may be several different post offices and/or sub offices within each
postal area including railway station post offices and the Stock
Exchange etc. I do not know whether these smaller offices had their own
postmarks, but certainly in the remainder of the UK almost all post
offices however small at one time franked their own mail. Certainly the
Stock Exchange had its own franking device( see literature connected to
the 1 shilling green Stock Exchange forgery).
These days most mail is franked with some generic postmark, for example
SWDO ( South West District Office) as part of the increasingly
centralised mail sorting methods.
Regards
Malcolm