I always thought Saturday was the better day for Borough Market, all stalls open etc. It is a lovely walk from Borough to SouthBank along the river. Takes 30 to 45 mins depending on how fast you walk and stop. Quite often we have lunch at Borough and then walk to Southbank for coffee and cake, before taking the ferry home.

But is the Southbank one your refering to the "Real Food" market? It's open every day over the Olympics, but I find it limited in its choices. Borough is a by far bigger, but have a look at the websites and see what makes you hungry and go there.