I have found that with only 3 or more mbps I get no iplayer buffering. My router / ISP normal speed is about 6- 7mbps with no problems. However I bought a new LG Smart TV, and set it up with a wireless connection. In the same room where I got 7mbps on a iPad the TV only showed 0.8 mbps and buffered constantly. I solved it in the end by either using the iPad connected to the TV with an HDMI lead, than bought a pair of homeplugs - one on the router and the other at the TV , than changed the network to wired and all was well. I suspect the built in wirless card is poor, but could not be bothered to argue with Currys or LG. Have you checked the download speed (s) on the device(s) you are using for I Player? I use Speedtest.net, as do many here.