Incidentally here's some recent research for anyone of an engineering set: https://arxiv.org/pdf/1509.00453.pdf

Yeah I kind of thought as much to be honest. When the broadband was installed the engineer brought the telephone line inside (it wasn't connected previously) with a thick cable, via a small junction...

Well, I spoke too soon. It was ok for a day or so then went back to being the same. I tried moving the PLC over to the other side of the room in a different socket but if anything it made it worse....

Even though the old Comtrend adaptor isn't compatible with my TP-Link, its filter works just fine. I plugged the router in via the Comtrend and now all is working.

Man I came to the right place. With such an (I thought) unusual problem I didn't hold out much hope of getting a helpful response. You guys are awesome!

That makes a lot of sense! I have an old set of powerline adaptors somewhere (80Mb/s I think!) which have the power passthrough - I will test your setup with these and if it solves the problem...