Does everything run OK on your ethernet-connected desktop? You get reasonable speeds on that machine?
If so, then presumably your problems are with the wireless capabilities of the TG582n. If you look through this board and Plusnet's own forum
you will find a lot of customers complaining about the wireless performance of this router. It seems to perform OK for some users (including in Plusnet's recent testing of a number of boxes, some of which had been returned by unhappy customers), and not at all well for a lot of other users (including me).
My own theory is that this product does not perform well under difficult radio conditions (multi-path, co-channel and adjacent channel interference).
My own solution was to replace the TG582n with an Asus router, which has the best wifi performance I've yet seen on a domestic product. I'm using the RT-N66U, but I'm on FTTC. The DSL-N55U
is the closest equivalent with a built-in ADSL modem. Not cheap though. Reviewed on TBB here
So if your problems can be narrowed down to wifi performance, it's worth considering replacing the TG582n with your own router.
PSS/BT Gold > Compuserve > Dircon > Zen > Be Unlimited > PlusNet Unlimited Fibre