Out of interest, why do Cannon Street trains only need 3 platforms, as against the 4 for Charing Cross trains? Don't the same arguments for needing 2 platforms in each direction for Charing Cross apply to Cannon Street?
Good question, and one I have been waiting years for someone to ask so I can answer.
The capacity constraint into Cannon St is the stretch through Boro Market Jn round the corner and on to the viaduct. In theory this limits services to a maximum of 22 tph each way. The fact that more get in during the morning peak is because of the succession of empties that come out via the Met curve to Blackfriars, this releases some outbound paths that are used by inbounds. Even so, the max peak flow in any direction is 25tph, with a lower number the other way. This is perfect for a tidal flow through London Bridge, with 2 in the peak direction, and one in the other.
Also the passenger flow is very peaky, there are very few passengers contra peak Cannon st to London Bridge. This means the contra peak dwell times can be less than peak direction (indeed from late 2016 it might be that some don't stop), meaning more trains can use the one platform.
Now, ideally, it would have been preferable to rebuild Met Jn area to get more capacity. However when it was looked at, it appears there is no way of doing it without widening the viaduct in some way. I walk under that viaduct twice a day, and widening it would make the new viaduct at Boro Market look like child's play.
Also to fit another platform in would mean widening the viaduct at London Bridge itself, and although that is possible, there would be a whole lot more compulsory purchase and demolition down Tooley St.
The key challenge now is how to keep the peak flow rate into Cannon St in the morning peak when the Met curve comes out of use and the empties via Blackfriars have to come out via LBG. As mentioned above, this might be achieved by causing a couple of contra peak trains to skip the London Bridge stop.