Hello everyone and thank you all for your help.
That's incredible, @J0hn, to hear that you're in Dalkeith, too! What are the chances of that?!
In response to everyone else's messages, I don't think the railway line is the cause of our problem. It's around 100m away from where I stay. Plus, it's not electrified but operated using diesel trains. I understand that there are probably electric cables that run along, but at least it's not like it's overhead wires and electric trains introducing huge outbursts of noise. Plus, the trains run here every hour, so I'd see more regular outbursts of noise, which isn't the case. I think the noise is local - see below.
From what I established, the tel. line in our area goes from the Exchange to Eskbank Toll and then branches off, into adjacent streets. From the Exchange to our pole, it goes underground all the way along. The cabinet is at the Exchange itself, and it's Broadcom.
I have a suspicion (and this is only a suspicion) that the cause of noise could be coming from one of the flats nearby. That flat is currently unoccupied and has been so for the past couple of months, meaning that our line has been more stable than before. However, the owners have recently been back and so it looks like that every time they're there, this outburst of errors occurs (there are there only on some days and at certain times). Previously, when that flat had different owners, they didn't stay there one winter and it was also a stable winter for us, which is why I thought this might be relevant. Other than that, when we had ADSL2+, it was interleaved in the winter (9db-12db) and back to fastpath in the summer (3db-6db). But we didn't work from home then, so it wasn't an issue at the time, and we didn't mind those disconnections while watching 'cooncil TV'.
This is of course speculation, but I wanted to ask: would it be possible for someone's boiler, hot water tank to introduce noise on the neighbouring tel. line? How far does the noise travel? Would it be intensified if there's a problem with one socket not being properly grounded, for example? Should I be looking for it in the nearby flats or also in the adjoining streets, in which case it's probably Sisyphean job? I've read reports of a whole village getting disconnected by a faulty TV. When I asked a British Gas engineer that came to replace the motor in our boiler, he said it was mainly devices like timers that could be introducing noise. (Below is another screenshot with a dip in SNR.)
The electric cables to the properties here run underground, too. When I walked in the street with the AM radio on, there was a distinct noise coming from that flat in question, but not others. But then, when you put the radio near electrical equipment, that noise is there too. So, is it the intensity of the noise that I should be paying attention to? Also, the issue is certainly local because the Exchange appears to see everything as ok.
We asked Openreach to get us a REIN engineer, but after they collected samples from our master socket, they said they didn't think it was REIN. Nothing got escalated, even though we asked for a senior Openreach engineer, as seemingly they don't exist in the company. Also, in their Terms and Conditions (or something similar), it says they're not responsible for any noise being introduced by customers, and if there is something like that, they don't usually investigate it, unless it was the whole estate/village.
I believe the neighbours also have problems (as they have told me so), but as I said previously, most are retired and don't mind whether or not their email doesn't immediately send to the local café to reserve a place (Dalkeith Palace), though one summer, when the windows were open, I did overhear one of them getting very frustrated with Alexa not wanting to play their favourite list. To get them to phone their ISP would be a major issue.
What I'm bitter about is that neither Plusnet nor Openreach are being honest with us. If they simply said that there's an HR fault and because the area is due to be upgraded, they'd not fix it, we'd be fine with that. Equally, if there's an issue with interference, then why not simply tell us.
There are also now blue markings near the poles (pointing to BT poles or BT manhole covers) on the nearby roads/pavements, which I presume are related to FTTP deployment. Virgin Media have announced that they are coming into the area, too, so I presume there's a bit of competition going to be going on.