This made me wonder whether there were any original tram maps digitised and on line (like the numerous railway and Underground ones). Apparently not; perhaps the network wasn't seen as a single entity to be mapped at the time. However, there is
this site which you may find more informative. Indeed, it makes me wonder how much research was involved in making this new, less complete, one.
The GS Tram Site splits London over several maps, and the single map does have the merit of showing the overall coverage more clearly. The lack of trams in the City of London isn't a big surprise, given the very busy narrow streets, and the priority given to getting office workers in and out. The lines map pretty closely onto the commuting pattern of Charles Pooter and his class. The tram desert over the whole of the West End is very striking, and surprising too.
True, this was where the more affluent Londoners lived, including those who worked in the City. There may well have been class-based arguments ("you can't expect people like us to travel in trams"), though I doubt very many had their own carriages - they would use cabs, I think. But by the time tube trains and electric trams arrive (1900s), I'm sure there were a lot of workers there needing to travel in and out. Of course the original underground lines did run through that area, but that big gap is still a bit odd.
Most of the Standard's comments are pretty silly. (Is there no explanation with that map?) I mean, only one crossing of the river? And by tunnel?
And how did the tram network affect building tubes south of the rirer? Only horse trams existed before the tubes were planned, and they were never a substitute for a railway. The first tube was open well before electric trams arrived, and getting under the river was one of the main reasons for going so deep. I prefer the traditional explanation - surface railways already covered the South pretty well (indeed, a lot of Southwark is carpeted with them).
The initial underground lines didn't reach there for the obvious reason; the early experiments with cut-and-cover construction across the Thames were a little disappointing. The first tube lines then did cross the river, and also the West End. The real question is why they didn't take over surface railway lines to go further out, as they did to the north, west, and east.