One of my favourites and a little known spot is The Point. It is a small park near Greenwich Park, but on the western edge of that ridge so gives fantastic views towards central London over the rooftops of Deptford.
From there you can just about make out Battersea Power Station in the east, though you do not get a clear shot of it, but then a practically unobstructed view all the way around to the skyscrapers of the Docklands. With a long lens you can get decent shots of the central London Skyline, and assemble a panorama from them, but with a wider lens you can have a lot of fun with the context of south east London in the foreground.
As a small local park it does not close, and though a little way out is accessible by the number 53 bus which runs 24-hours between Lambeth North and Plumstead, connecting with the DLR at Deptford Bridge, the Overground at New Cross, and Underground from Elephant & Castle.
The nearest railway station is Greenwich about fifteen minutes walk away. But being downhill it is better for leaving than arriving when you have a bag of gear and a tripod, so the bus is better.
It is also not illuminated, which though helpful for photography you might want to bring a torch to see what you are doing. You can see the park (and nearby bus stops) on Google Maps:
The 53 bus also serves Woolwich, where if you walk along the river towards Charlton you can get some great shots combining the Thames Barrier, the O2 Dome, and Canary Wharf. Combining the two can make for a fun evening.
(Both shots my own, but a bit dated now given the obvious lack of various City skyscrapers and the cable car. But just writing this has made me want to go back!)