Hi, and welcome RR7.
Firstly, let me assure you that the 'line sag' is nothing to be concerned about. It's actually better for the cable that it
does have a sag, as if it were bar-tight (like lots of engineers try to achieve), then during high winds the stresses put upon it are far more advanced than that of a 'loose' cable. We can sometimes then get high-resistance type faults or even short circuits. I have to say though, they are extremely rare occurences. So, short story, long
don't be worrying about the overhead dropwire feeding your house.
Now, the symptoms you are describing are inherrent with developing high-resistance faults. This could be an underground joint closure getting wet, or corrosion on your internal sockets, even a poorly connected crimp that we use for joining wires together. If my eyes don't deceive me (and they can these days), the DP Block (the box at the top of the pole) is the type that tapers upwards and they are a beggar to slide on or off, especially if there are lots of wires connected, which it appears there are from your photo. It is very easy to trap one, or both wires when sliding the lid back on. After a period of time passes, corrosion will beging to eat away where the trapped wires are, causing a HR fault.
Another cause is if your internal installation is subject to star-wiring and one or more internal sockets are not filtered. This is all guesswork though, and your first port of call would be to locate the Master Socket (the first socket where the dropwire enters the house) and there will be a test socket you can plug your router and into (unscrew the frontplate and remove carefully) to see if the problem still exists. This will determine whether the issue lies inside your premises, or on Openreach's network.
Regards
BS.