Go to Crystal Palace, marvel at the lack of both crystal and palace. How did a greenhouse burn down anyway? Go see the wrong-o-saurs, though some of them are in dino-restoration hospital at the moment. Gaze out at the best view there is of London. Cross the road and soak up the views of Croydon skyline. Then cross back, quickly, before it nicks your eyeballs.
Borough Market is super-annoying crowded these days, but there's loads of street-food-y markets dotted around (walk a bit further to Maltby Street and wash down lunch with something from Anspach & Hobday). Sometimes just wandering is the best plan, the touristy stuff sucks, I've no idea why people fly around the world to visit the same shops that in every capital or, the horrors, to queue for the Hard Rock Cafe.
Scientists have proved that tourists won't immediately die if they leave zone 1. Just ensure you take an environment suit and self-contained air supply.