So, I walked it home, and that weekend bought a new axle and so forth and fitted it. It wasn't perfect, but it worked. I've had to reattach that a couple of times - the nut occasionally begins to work loose and the wheel "drops" in its housing - but it's not broken again. On the other hand, the back wheel's got more and more precarious over time; the brakes got jammed against it at one point, needing some complicated reworking to fix, I've had to wire the back mudgard to stop it chafing against the tyre; and now the whole wheel's inexplicably wobbling from side to side, about half an inch of yaw each way, no matter how firmly I bolt the axle.
So, today or tomorrow, I'm going to strip it all down again and see if I can get it working anything like smoothly. Unfortunately, I suspect this is a pretty deep-rooted problem, and the wheel itself - or the mounting point on the frame - might be screwed.
So, the actual request here: this is probably beyond my capacity to fix. Can anyone recommend a bike repair shop in Oxford (preferably not too far from South Oxford, since I'll need to walk back), who'll be able to look at this and fix it for a reasonable price for me, or alternatively tell me upfront if it's beyond help? I should try and get this fixed before I have to commute again...