So, I booked a flight to Japan (yay!) with British Airways. I went onto kayak.com and found the cheapest flight I could find, which was (iirc) 540GBP. The catch is: this flight begins in Amsterdam, not in London, even though there's a transfer in London. The cheapest flight direct from London was over 700 pounds.
So I booked the cheap Amsterdam flight, since it's still way cheaper for me to fly to Amsterdam one day, then take a plane back to London the next day. It's basically a free trip to Holland. I did try to call BA today to see if I could cancel the first flight from Amsterdam to London to see if I could skip the silly round trip, but that was not possible. The person I spoke to told me that I had a 'special action price ticket' something or other, and the only way for me to start the trip in London would be to re-book at normal prices, which would cost over 1000 pounds.
I tried to point out how silly this was to her, and that BA would actually make more money if they accepted my flight's cancellation and try to sell it to someone else, but they wouldn't listen. Bureaucracy I guess. Or they just really really want to prevent English people from going to Japan. Weird.