My understanding is that trains to and from Cannon Street will only have two tracks available to them at London Bridge and there wouldn't be enough capacity if trains stopped at London Bridge. Hence they'll pass straight through instead. Whereas trains to and from Charing Cross will have three tracks available to them which does provide enough capacity to allow stopping.
However platforms 4-9 seem to be well on their way to completion and so why can't trains to and from Charing Cross use platforms 7-9 and trains to and From Cannon Street use platforms 4-6? This would mean that Charing Cross and Cannon Street services would both have three tracks available to them which would allow all services to stop at London Bridge.
Thanks
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Globe Rowing Club
Rowing in Greenwich since 1923
www.globerowingclub.co.uk