Postal counties are pretty well established, based largely on
administrative
counties of some decades past. People, not surprisingly, quote where they
live as where they are addressed, hence people in Bexley say they live in
Kent as that's what they usually quote as their address.

Indeed, and there are other variations. Edmonton has had a London postcode
since the mid-1800s, about thirty years before it came under the control of
Middlesex County Council, and about century before it was ever controlled
by any London administrative body. Some other parts of the London Borough
Of Enfield still have Middlesex in the postal address despite having a
similar history.

Post is really based on Post Towns and the Post Code. The county you see on
your postal address may well be that of the post town rather than your own
town. Your postal address can include a county that your town has never
been part of geographically or administratively.

Describing locations by administrative areas, particularly as they seem to
change so relatively frequently in the UK, makes no sense to me, though
this
seems increasingly common.

Absolutely, and it is not helped by the Ordnance Survey using administrative
boundaries on their maps.

http://www.abcounties.co.uk/ gives a good background to all this sort of
thing.

Plus, I don't understand why the "Greater" is being lost from "Greater
London". Greater London, to me, means real London plus lots of fringe
areas
that aren't really "London" but close enough to be administered by it.
However, organisations such as BBC London appear to ban the phrase unless
it's in a name of an actual body, eg the GLA.

When we had the GLC the term 'Greater London' did seem to be used a lot
more, though that has never been part of any postal addresses. Now we have
Greater London Authority the term is just as well defined, but we only
really hear mention of the Mayor Of London and the London Assembly that
comprise it.