I started the day at the airfield, where I took the plane out for an hour of circuits until it got too bumpy to have fun.
When I got home, I turned the water off and took the hose fitting off the bottom of the toilet, and we went out and got parts - a new tap fitting, hose to the inlet on the toilet and ballcock. Of course, it's still filling itself from time to time, so the problem seems to be the flapper valve is leaking (as the old ballcock had been hissing on and off, I assumed it was the ballcock, but that all needed replacing anyway as the washers were disintegrating).
In the evening, I went back out to the airfield and took the plane out for a flight. It was pretty bumpy and windy, so I didn't do much, and headed home after about an hour.