In my not very technical world I'm really not sure. How could I tell from the symptoms whether it was sync speed or throughput and what's the difference anyway?
The sync speed is how fast bits are being pushed down your phone line to the equipment at the local telephone exchange. It will be reported by your modem through its management interface, and to your ISP through the BT wholesale API.
The actual throughput is what you measure by sending data to and from somewhere on the internet, and will reflect the tightest bottleneck on that particular route. In an ideal world the bottleneck should be your ADSL line, but I know that Plusnet - like most ISPs - oversubscribe their network and apply traffic shaping to maintain acceptably reduced performance (it's a simple case of getting what you pay for, and to their credit Plusnet are honest about exactly what they do). Sometimes there's a fault that creates a bottleneck elsewhere - perhaps in the BT network between your exchange and your ISP, or in the wider internet between your ISP and whatever you're downloading from. That sort of thing can be hard to track down, without advanced diagnostics running in multiple locations.
If you're getting poor throughput but the line sync rate is decent, then you know it's not a problem with the local loop, and any mucking about with ADSL filters and such is irrelevant.
The telephone has lost it's hiss and crackle now - I wonder if the issues are related?
ADSL bleeding through onto a voice phone sounds like a hiss. That could well be a symptom of a dodgy filter (or other wiring fault), and will affect the sync speed.
If you disconnect the ADSL modem, that hiss will stop after a couple of seconds when the exchange equipment decides there's nothing to talk to and gives up. If there are still crackles and hisses on the line, and you've eliminated all your own wiring (and you're using a good old-fashioned wired phone), then you should report it to your telephone service provider as a voice fault. Don't mention broadband. That's the most reliable way to get line problems fixed, as BT will try to play the blame game with broadband faults, but get on and fix faults reported for voice. It's the same wire, so fixing a voice fault usually improves the broadband performance.