Thanks for all the information, it's helping me to diagnose the issue. I'm doing some more investigation in the meantime.
I should have mentioned previously that I had not plugged a filter into the second telephone box and so the electrical inference was likely to be the ADSL connection (i.e lots of retro 56k modem type noise from the early-90's

. Anyway, I unplugged all devices apart from a wired phone and did a quiet line test. The second telephone box seems to be slightly noisy than the main one, but it's still pretty quiet. I can only hear a very low volume hiss and some occasional clicking noises. I can't hear anything at all from the first box, but the location is slightly noisier, so I can't be sure.
I should say my mobile stats have improved since my initial post. From experience, it's just temporary though

The SNR Margin seems much higher at the moment. I tried to trigger an issue by calling the phone several times, but it seemed to have no effect.
Operational Mode - G.DMT
Upstream - 800 - 800
Downstream - 4000
SNR Margin(Upstream) - 11
SNR Margin(Downstream) - 8.9
Line Attenuation(Upstream) - 28
Line Attenuation(Downstream) - 53
Interestingly, the SNR dropped to 6.3 just five minutes after reconnecting, although this was before I started testing calls. It's up to 6.9 now. As a guide, I've seen downstream speeds of 5000 as a maximum in the past.
I've started using both RouterStatsLite and DSLStats so I should be able to post some results soon I hope. I realise they overlap somewhat, but I started with RouterStatsLite and DSLStats seems to do more, so I figured I'd leave them both running.
I'm considering calling out BT again to remove the connection to the second box (only the cost puts me off, which is why I'm hoping to get as much a guide as possible if it'll help or not). Presumably, this would resolve that particular issue? If it's just a matter of disconnecting it, then it should be fairly simple, although it'll require a ladder, the line seems to originate near the roof. I should say that most of the long wiring on the second box is internal to the house and wouldn't need touching I think if it was disconnected from the source.
I'm not entirely sure that the second box is causing much of a problem though apart from a potential loss of speed. But given I can't really explain the problems I'm having now, anything is possible