I contacted Epson to see what they could do - they could collect it and service it for £200, but that seemed like a lot of money to spend on a 5-year old printer. After a bit of online searching, I decided that it must be the waste ink tank that was full. Rather than spending £600, or £200, I ordered a waste tank kit for a tenner that essentially bypasses the internal waste tank.
The printer is working fine again, but the really worrying thing now is, since the waste tank is now outside the printer and visible, I can actually see how much ink is wasted every time I have to change a cartridge! For what is said to be the most expensive liquid on the planet (mine works out to around £1 per ml), that's a lot of waste!
Do you think I can bottle it and sell it back to Epson?