Numerical and alphabeticised lines
My design suggests abandoning the present names for the London Underground lines and recategorising them numerically, in the manner of European metro systems. The numerical order is based broadly on the sequence of dates that the lines were opened or created, from Line 1 (Circle Line, a section of which was opened between Paddington and Farringdon stations in 1863) to Line 14 (Waterloo & City Line, which was incorporated into the Underground system in 1992).
I have created several new lines from existing ones, particular those which have multiple branches: Line 3 from the Uxbridge branch of the Metropolitan Line; Line 6 from the branch of the District Line between Edgware Road and Wimbledon; and Lines 7 and 8, the former given a gold colour, by separating the two branches of the Northern Line.
I have also given each of the London Overground lines, including those lines projected to be incorporated into that network in 2015 a separately distinguishable colour in place of the presently homogenous orange, and labelled them A-F. Other lines included are the new Crossrail line, the Croydon Tramlink, Docklands Light Railway and the Emirates AirLine Cable Car, each of which are represented by a coloured symbol with the TfL roundel rather than a letter or number.
Station symbols and representing accessibility
The traditional 'tick' marks for stations have been replaced by circles centred on the lines. This is a design detail that TfL presently use for their bus network maps.
The issue of representing station accessibility (i.e., whether stations have step-free access) which appears to be a major preoccupation for TfL's map designers, has been addressed by featuring a simple range of blue or white circles to represent accessibility rather than wheelchair symbols which are becoming increasingly obtrusive on the present map. For a further explanation, see the next image caption.
Symbols
I have included two new symbols: an encircled 'i' to represent locations of TfL Information Centres, and a star to represent a station that is closed on Sundays (presently only Cannon Street). I have retained the National Rail and boat symbols for mainline and riverboat connections respectively, and the dagger symbol to denote a limitation to a service (although I have kept the explanation in the key to a minimum - further information on each affected station could be listed elsewhere).
Typeface
I consider the various derivatives of TfL's famous Johnston typeface that are freely available on the internet to be of poor quality, therefore I chose to use Myriad Pro as a substitute for its clear appearance and legibility.