Borough Market is what most Londoners tell visitors to do for food, and they're right, and also the market is nicer if you come to it from the wrong direction. Walk in via Bermondsey Street and Maltby, and by the time you get to Borough you'll have already eaten, the crowds will feel less oppressive, and you'll buy only the good bread.
Start at London Bridge, duck through Hay's Galleria for the covered Victorian glass, and turn south onto Bermondsey Street. The street is fifteen minutes long and has quietly become the nicest stretch of independent shops in Zone 1 — a good coffee place, the Fashion & Textile Museum, White Cube for some free art.
Maltby Street for lunch — small, bouncy, the Ropewalk stalls do the best unfussy street food south of the river. Then west into the back of Borough Market, where you'll arrive full and can do a walking lap for the atmosphere.
Finish at Southwark Cathedral for five minutes of silence before the train home.