Finally got through to them on the phone (was trying to do that originally, but lines were busy presumably with other people doing the same). They confirmed the delay was because the plane wasn't due to arrive at Gatwick until after 6pm. They said that they were keeping check in desks open through the afternoon, but that we should check in by 5pm at the latest.

So I guess we'll turn up at 4pm and hang out in the lounge for 3-4 hours. Not ideal, but better than the 10 or so hours we'd have been looking at otherwise. Thanks for response.

Thanks for info on compensation. Hopefully €600 each should soften the annoyance somewhat.