I also have a LG smart TV. Although on my network I get about 9mbps, on the TV I get less than 1, and the BBC iPlayer on wi fi stutters to the point of not enjoying it. I actually phoned LG who more or less admitted a problem with wireless. I also have a iPad and a laptop with an HDMI lead connection so now I use one of them to watch catch up on the TV from any of the other catch up services.
Sony Xperia Z5 review: Hands-on with the phone which the Z3+ should have been