I washed my mower - including the engine, and now it won't start. When I turn the key I get a clicking sound. The lights come on but the engine won't turn. The 20a fuse appears to be OK.

Hi,
Somewhere you have compromised a connection. First clean the battery connections (always remove the negative cable first to prevent arcing) to make sure they are good. While the battery is disconnected, you may wish to clean the solenoid connections. They (the battery and solenoid "live" in proximity to each other on your model.
Then carefully unplug the ignition switch and reconnect.
Hopefully on of the above will cure the problem, assuming that simply allowing the machine to dry on its own does not.
Peace,
Clarke