Hm.
Errant flushed item hypothesis: I honestly cannot think of a single person who would have flushed something unflushable, and I cannot think of a single thing that we have flushed that isn't toilet paper or, uh, biowaste. We don't keep anything in that room except toilet paper - toothbrushes and the like are in the bathroom. We don't have children or many overnight guests. I'm not saying it's definitely not true, just that it's not an obvious answer. How can I check? Or what would I do if it was?
Tree root hypothesis: Yeah, I think I can confidently say that this is incredibly unlikely. Toilet is on the first floor along with bath and two basins; sink, washing machine and dishwasher are on ground floor. Only the toilet ever has any problems. Also, my neighbourhood is a concrete wasteland with very few living things except people and vermin.
Toilet paper hypothesis: Intriguing. In the few months since the problem started, we have been through three different brands of toilet paper because my preferred brand has been unavailable twice. No data available on correlation between brand and clog, but it's certainly possible.