From TfL’s weekend travel information email:
Southern Railways are operating their normal Saturday service from Forest Hill to/from London Bridge, Victoria (via Crystal Palace) and Coulsdon Town as well as their normal Sunday service to/from London Bridge, Caterham, Tattenham Corner and Crystal Palace.
Saturday
Forest Hill to London Bridge at 0558, 0628, 0643 and 0658 then at 13, 28, 43 and 58 minutes past each hour from 0713 to 2328 then 0001 and 0034
London Bridge to Forest Hill at 10, 28, 40 and 58 minutes past each hour from 0610 to 2358 then 0020 & 0035
Sunday
Forest Hill to London Bridge at 0728, 0746, 0807, 0815, 0829, 0845 and 0859 then at 13, 29, 43 and 59 past each hour from 0913 until 2313 then 2346
London Bridge to Forest Hill at 13, 28, 43 and 58 past each hour from 0713 until 0858 then 12, 28, 42 and 58 past each hour from 0913 until 2312 then 2350
For other routes see National Rail website:
