Indeed.If you say just the postcode,that hasn't really been the case since 1965.Then you have the old County of London.Up until 1965,both Tottenham and West ham would have had Middlesex and Essex respectively in their postal addresses(though i dont think either used it) .Personally i think there are two London boundaries,the square mile and modern Greater London.
Also, the london postcode originally went out to the edge of Enfield (freezywater) ,in the north, Ilford in the east,Croydon in the south and Hounslow in the west,But was scaled back and numbers added as it was deemed too big to administer.
London had a NE and a S post code then as well, but after being scaled back they were given to Newcastle and Sheffield.There are still a couple of NE street signs in Hackney, i believe.
I have a lot of time on my hands...