On the Tufte discussions site, Mike Hunter reminds us of the redesigned London tube map that Paul Mijksenaar produced in 1983 with his research group at Delft University.
Despite the lack of quality in this scan, you can see how they retained a diagrammatic design for the outer areas (to aid with the "getting-in/out of London" function) and switched (back) to a topographic style (to aid with the "getting-around London" function) for the inner-city area, with zone 1, or something like it, seemingly the boundary.
Scanned from his Visual Form (1997), 010 Publishers, Rotterdam (amazon UK | US). The original is from: Mijksenaar and Vroman, 'London Transport Map: A Delft Project', in Typos, 1983, no 6, pp36-40 [It's at St. Bride's print library, catalogue q4934030, reference only].
For metro-type systems with few stops asdn long distances in-between [a radically schematized map] is not some much of a problem. But in the case of fine-mashed transport systems like tram and bus networks, it is vitally important to retain a recognizable reality [...] In the Delft version, underground routes in the center of London are rendered topographically, those outside diagrammatically. In the city center the map is augmented with references to major landmarks like parks, places of interest, and museums. This enables tourists, for example, to plan their visit better and avoid bizarre detours. [p6]And apparently it was rejected with a stiff-upper lip by London Transport's management .
Mijksenaar's Signs of the Times article, on designing airport signage, and the creative conflict between architects and information designers, is well-worth a read.
See also: the Way Out tube map, and the London track map. And our tube map with walklines and underground drawings one and two.