Trains from ED to London Bridge are fairly reliable and frequent. Whether you get a seat depends on when you travel - between 8 am and 9 am you probably won't, unless perhaps you go right to the back of the train (and are happy to be at the back of the queue to go through the ticket barriers at London Bridge). Seats in the evening, from London Bridge, usually aren't a problem, and the trains, even if you're standing, are rarely as crowded as tubes at the same time. For Shoreditch, you may be better getting the East London Line overground from Forest Hill, but it could depend on where you're starting from in East Dulwich. Getting on to the Northern Line at London Bridge isn't fun in rush hour. For Charing Cross, you can cross platforms at London Bridge and get one of the very frequent trains that go through and on to Charing Cross.