Reading that London Reconnection article. From what I understand.
January 2015 to 2018
Forest Hill is going to lose some trains to/from London Bridge while they construct the Bermondsey dive under between New Cross area/London Bridge. Timetable is not out yet.
This will be slightly compensated by an extra carriage on the Overground. And maybe an extra service or 2. But nothing confirmed. However, you're taking away an 8-10 car train for a 5 car.
From 2018
Forest Hill will have 8 London Bridge trains (up from 6).
London Overground could be 6-8 services.
Basically....the next 3 years is going to feel pretty busy and disrupted. Atleast we don't have to get on at Brockley!