2 weeks ago - no trains
Last week - no trains
This weekend - no trains
Weekend of 24th - no trains
Weekend of 31st - overground only
Weekend of 7th - overground only
Southern Claim to be running on 31st May but not on 1st June
So to continue this at least on Overground (no information on Southern beyond July):
14 Jun - All running
21 Jun - Southern Only
28 Jun until 9th Aug - overground running
6th,19th,20th July, 3rd Aug - overground only
16 Aug - no overground (don't know about Southern)
End of August Southern go crazy for a week (no trains for a whole week) but Overground will run
6 Sept - no overground (don't know about Southern)
13 Sept - no overground (don't know about Southern)
20 Sept - overground running (don't know about Southern)
27 Sept - no overground (don't know about Southern)