I know from my railway experience that Joan's reply more or less is the correct technical reply. However, there are issues that have not been addressed in that reply.

The main reason why the trains from Forest Hill do not continue to London Charing Cross is that with the December 2009 timetable virtually all off peak 'fast' trains call at London Bridge in addition to their being a few additional suburban services. Every train towards London has to stop in Platform 6 at London Bridge. In the other direction those trains can be shared between Platforms 4 and 5. However, you have to stop trains in both directions or not at all.

Essentially the DfT effectively took the decision a couple of years ago that the capacity released by the diversion of the Eurostar trains should be given to Southeastern trains (meaning more trains at London Bridge). Since it was also decided by the DfT that all trains in the off peak should stop that London Bridge that effectively sounded the end of the Southern Trains to London Charing Cross.

Of course had the platform lengthening at London Bridge that was carried out in the early 1990s included a new Platform 7 (so that all trains towards London Charing Cross could stop at London Bridge) then it is likely that Southern trains would still be running to London Charing Cross.

Obviously it was the Conservatives that cut that proposal by BR. In addition it was the Conservatives that stopped the work to allow 12 car trains on the Dartford services. That work was never restarted by Labour and has still not been started, although it is now planned to be done in the next 5 years. With trains being limited to 10 cars that is partly the cause for the need to run more Southeastern trains, so preventing the Southern trains from operating.

I would hope that people remember those facts when they vote in May if they vote for Labour or Conservative.