The quickest way to get pretty much anywhere in London is by bike and the Boris bikes (or Santander cycles as they're properly named) are sprinkled around everywhere through London making it easy to pick them up and drop them off wherever you're heading to.
Boris bikes are a ridiculously cost effective way of getting around London too, it costs £2 per 24hours to hire the bikes and as long as you don't keep one for longer than half an hour the rest is free. You can pick up and drop off Boris bikes an unlimited number of times in your 24hr session as long as you keep your journeys to less than half an hour a piece and travelling pretty much anywhere in London takes less than 30mins by Boris bike so it's easy to keep it free.
London's policy on wearing helmets while riding bicycles is relaxed so you don't need to prepare anything to start riding. Just rock up to a santander bike station with a valid credit card, follow the prompts and you're away.
While the London roads can look scary, drivers are pretty accommodating to cyclists and because central London has a 20mph speed limit (and ridiculous traffic), you're normally going the same speed on your bikes anyway.
Boris bikes are available to hire 24hrs and they're cleverly equipped with front and rear lights that automatically come on when you pedal so they can be ridden day or night relatively safely.
You'll see Boris bike stations pretty much everywhere when you're walking around London. If being touristy you can pick them up from where you're staying and drop them off at the Tower of London before heading to tower Bridge. If you are stuck to find a bike station then get yourself the "city mapper" app on the app store as it does a much better job of pointing them out than the official santander app!
...Oh and if you're wondering why they're called Boris bikes it's because they were introduced under the mayorship of Boris Johnson.