Have a look at your VDSL plots in DSL Stats and you will see notches with zero bit loading where the major AM transmitters broadcast ... so even miles away, it can have an effect. Close up, it can cause wideband issues.
Whilst not directed at me, that suggestion has spurred me in to seeing if I can get some more detailed line stats from my modem – I don't generally have access to that kind of thing 'cause it's a router being used as a PPPoE bridge. Anyway, I found it has a CLI so reset the modem/router to gain access to it via telnet, and have been able to obtain bit loadings and per-tone SNR info. It doesn't look like I can upload attachments here but suffice it to say there're quite a lot of blips and troughs in the data, more than I'd expect for a line that's mostly underground and no more than 1km from the exchange. The largest of the troughs lines up perfectly with the 1584kHz radio station: it completely knocks out three frequency bins and reduces the throughput of about 30 more. There're a couple of other noticeable troughs (affecting approximately half as many bins as the one I can hear) and they both tally with MW radio stations, with several other narrow blips too.
I've also been able to obtain a downstream attenuation figure, which is reportedly about 20dB, which does seem a bit high for the expected line length. Do people think that's going to be caused by the radio interference issues or will be that be down to something else entirely (like the old GPO box)?
Anyway, thanks everyone for your input. I feel like I might actually have a fault diagnosis now, which will hopefully make it slightly easier to get fixed!