Would depend on date. Greenwich was in the County of Kent until the formation of the London County Council (1890ish?). The term "London Borough" only came in after the re-organisation of local government in the 1960s which created the GLC. This took in a much larger area than the old LCC (London County Council) and merged many smaller boroughs into the current big ones. It is possible to recognise those bits which were LCC because they all kept the original London postcodes, SE, SW etc. Places like Croydon, Coulsdon, Merton, Beckenham etc., have new post-codes (CR, SM and so on) but often still use Surrey, Kent etc. in their addresses which was the case before the formation of "Greater London". Hope this is useful.