Abbey Wood is two stops on the train or a short bus ride from Woolwich Arsenal DLR station. You can then catch DLR into Central London. It will be slower than the train into Cannon Street but you can use an Oyster card.
The most convenient and probably cheapest ticket would be a Travelcard on an Oyster.
DLR will take you into Tower Gateway but you may have to change. For the west end take DLR into Bank and change to the Central Line.
Woolwich Arsenal pier is also not far away. Boats are not as frequent as other piers but run at weekends and peak times.
All the info can be found on tfl.gov.uk and includes maps of boats, buses and othe rpublic transport.