I came across the Portland Streetcar. http://en.wikipedia.org/wiki/Light_rail
They decided to implement a tram that is lighter than Light Rail. They’ve spent $130m (£110M) for 5km of streetcar. The spec involves digging down 30cm for new tracks rather than 45cm for light rail. They also largely use traffic signals which are cheaper than special track signalling and don’t involve central signalling boxes etc.
This seems the perfect solution for a new tram from Peckham to Waterloo station or even London Bridge (connecting with the shard) via Elephant&Castle. The cost is such that even Southwark could choose to borrow the money for this on its own or use planning gain but it takes some big imagination and political will.