Beyond a bucket under the sink, that is. Has anyone got some ideas that don't involve drilling holes in the wall or putting permanent fixtures in the garden?

My kitchen sink clogged up a few months ago. I replaced the plumbing under the sink, but the problem was further down the line. I did not have time to fix it immediately, so in went a 5 gallon bucket for the best part of a couple months. I was quite surprised to learn how little water went down the drain. I was expecting I would have to dump it a few times a day. A couple times a week was all I needed, and it was rarely full unless I did the dishes.

A clothes washing machine is the easiest to capture in an existing house, rental or not. The machine has a pump for the water discharge, which means you can have an outlet for it at window height. I would run a 1.5 inch PVC pipe out the window and to the tree/ location you want grey watered. You can even have several pipes out the window for different locations, just move the washer discharge to whichever one.

For anything other then a washing machine it will be harder, as the pipes are covered in the walls. I suppose you could remove the p-trap under a sink and rig up a garden hose fitting and run that outside, but you have to make sure you maintain a downward slope, and be careful that nothing but water goes down so it doesn't clog the small line. Also, if you disconnect the p-trap, make sure you properly (temporarily) cap the drain that continues into the wall, so you don't get sewer gas into the house.