I disassembled the washing machine, removed a sock clogging the water pump, plus a couple more socks in the basin beneath the main tub (future clogs waiting to happen), and reassembled the whole thing.
Now it's working again! Moral of this story:
Don't overfill your washing machine, people!
(Alternative moral: Appliance repair is in every one's reach, thanks to the internet!)
How can I take apart my washing machine, you're probably asking? Watch this video: