Hi
I dont wish to sound like I dont appreciate your issues, I do, but from what you have said, moving to a new ISP, will more than likely culminate in the same issues. I have thought on numerous occasions of moving ISP for various reasons, but resisted, mainly because of these forums, and some very helpful CSC staff, Other ISPs just dont have this. If you give all the info, the more knowlegable chaps on these forums, will give you a weath of advice, and fault finding checks. You are correct in that your speeds nowhere near match what you should be getting. Just a couple of other things, that you may or may not have checked....
What package are you on, have you gone over your allotted bandwidth?
Do you have a Master Socket with a removeable faceplate. If so, are you connected to the test socket behind the removeable faceplate. This takes any internal wiring out of the equation.
Try the quiet line test, at various points during the day and night, Dial 17070 option2. If you hear any noise, crackels hissing etc, then there is a voice fault that will affect your broadband too. Report to your voice provider, but DONT mention broadband.
Do you get alot of disconnections of sync. If you dont know, Plusnet should know from their radius logs.
PlusNet are just trying to ensure its not a problem with your setup. If they call out BT, and they find its your equipment at fault you will be liable for a charge of 144+VAT, regardless of what ISP you are with.
I do hope you get things sorted, and I am sure the chaps on these forums will do all they can to help.