>>After that an amble along the Southbank
I did a Southbank walk a few months ago, from Westminster bridge all the way to Tower bridge.
There is a footpath all the way along to side of the river (apart from a couple of minor detours where you cant get along the river edge).
There is so much going on along there - London Eye, Festival Hall, Tate Modern (free to get in and great view from the cafe at the top), Globe theatre. Borough Market, George Inn (National trust owned pub), Southwark cathedral and so on.
Borough Food Market is busy on a Saturday, but an amazing place.
http://www.boroughmarket.org.uk/
On a Saturday all along South Bank there will be loads of people and a lot going on and none of will cost you anything (unless you pay to go in an activity of course).