I think the Greenwich property is more mid-scale (for the UK) but of course it would also be significantly cheaper. My observations about the three choices (Bankside vs Hart vs Gantry) is that Bankside is the only one which is a full scale 5* property, with an EL and the spa downstairs, so it is really in a higher class of hotel than the other two IMO. Gantry is in Stratford which is basically a huge Westfield shopping mall with excellent train and tube connections around London, particularly the east side, and if you are interested in seeing the 2012 Olympic Games area then that is there too. Otherwise it is not really a place to wander about. Bankside and Hart are both in neat areas, the former more touristy but very much in a pedestrianised area along the Thames, the latter more quirky, with more car traffic, but both are fabulous for just wandering around.

I do really like the whole of the east side of London (east-central and further east), which is interesting and far less crowded. A lot of walking and looking at the architecture both old and new.