Thankfully, there were lots of people around to help guide me:
My gears have been making awful noises as I pedal on the highest one up hills, and someone suggested they needed oiling. Did they ever. They're now well oiled and silent like ninjas in the night.
My rear brake hasn't been working. I won't show you a photo of how badly frayed the brake cable is (it won't last much longer...), but that ultimately wasn't the main barrier. That would be the misalignment of one of my rear brake pads. A bit of adjusting and ta-da, I have rear brakes again.
Anyway, how to bike to work.