Even a fairly poor wifi link is likely better than your broadband speed.
I get a good broadband connection, I'm near the exchange and see a (measured) 8Mbps.
Wifi is (mostly) 54Mbps, which you'll never see realistically, but you only need to get 3Mbps to stream HD iPlayer (less for SD) and you'll get that easily.
You do get better classes of ethernet cable, and as you suggest chokes (no magnets in them, it's just ferrous metal) may damp interference. You may be able to clip some off something else you have already to try out.
Another possible issue could be grounding, if the two devices are on different parts of the mains ring. Can you try plugging them into different sockets and see if it helps?