Right, I gave up on my previous attempt to show every rail service in and around London....it simply became far too complicated, so I've resorting to just showing rail routes and stations, and this is what I get:
Please note that this is still a work in progress. The south and southeastern rail network is currently absent, while no light rail, bus or ferry networks. More importantly, not a single London Underground line is shown, so you can see how big the commuter rail network is in and around London.
It also looks a bit messy (quite hard to judge properly how many stations and lines - there are two separate maps in real life) and while there aren't any station names, there are stations (if you look close enough you can see what will be the 1,200+ heavy rail stations of London and its environs.