Wrong, aP; it now works on Overground services. Not main line services, but local branch lines. Not sure if London Bridge to Greenwich is included, however, but more local train lines are being included in the Oyster scheme.
It is a confusing area, however.
Oyster on rail services
And DLR to Greenwich, from Bank or Tower Gateway, does not take a week and a half! It’s a fun journey for youngsters, specially if they can sit at the front of the train.
Oyster card will also get you a discount on the Riverbus services,which go from the Thames Flood Barrier at Woolwich, to the Tate Britain. It’ll only be £3.50 for adults, I think , with an Oyster card.
Transport for London