If you want to get to one of the main tourist spots (e.g. The Tower of 
London, Harrods, St Pauls Cathedral, etc) then visit 
<http://www.londontransport.co.uk/> and download their "Visiting 
London" brochure. The brochure is in Adobe Acrobat format so you'll 
need to download a copy of the FREE Acrobat Reader from 
<http://www.adobe.co.uk/>   

For rail journeys visit either of the following websites:

<http://bahn.hafas.de/bin/detect.exe/bin/query.exe/e?>
<http://www.railtrack.co.uk/travel/>

IMO, the German site is the better of the two because it shows you 
times at all of the intermediate stations and a little map as well if 
you want it to. There's no need to worry about not understanding it as 
that URL is for the English version of the page. (-:  

There is one problem with it, however, and that is that it doesn't have 
details of Engineering Works so it can tell you to get a train that 
isn't running, so *always* double-check on the Railtrack one or on 
Ceefax page 491 nearer the time.