The double decker bus tours are definitely a good option - you can buy tickets from various places around london. If you are into sports then seeing a football game is great - but good luck getting tickets to any premiership game that doesn't cost a fortune! London zoo is nice - but if you don't have kids I wouldn't put it at the top of any to do list. There are so many things to do in London - if you are there for a Saturday morning catch the tube to London Bridge and go to Borough food market - it is amazing and something different. From there you can walk up or down the river. The National History Museum, Science Museum and British Museum are all free entry and all really good...
Once you have done your bus tour and found your way around the city - get a map and walk! London is deceiving - a lot of things are closer than you think and London is such a great city to walk around. Enjoy - if it the weather isn't too flash it is a great city! And if you want to feel like you are out of a big city - go down to Richmond - beautiful part of south west London on the river - possibly also a good place to find a hotel as it is between London and Gatwick. Travel safe.