We've found some new evidence on the causes of the strange incident with our bathroom door. John had a look in the bathroom after we got back from the pub tonight, and we found footprints on the bath and the window sill. The ones from the window sill could conceivably have been made a while ago, but the one on the bath has definitely appeared over the last day or so.
So it looks like our strange door-closing-by-itself mystery was actually some plucky burglar. I say ‘plucky’ because the only way s/he could have gotten in would be through the bathroom window, which is one of those ones where the small top part opens, but most of it doesn't. They must have been taking their lives in their hands to get through that, and have been pretty good climbers to do it without making a noise. We think the noises John heard were the guy trying to escape through the window.