So the DrayTek 2862 AC is connected directly to you Plusnet DSL currently ? and TV is connected directly (no AP,s Switches) to DrayTeK etc.
What firmware are you currently running and make sure LG TV firmware is upto date as possible ?
If all above are updated, then sounds like the basics are covered, then maybe look to ensure the TV is getting the correct IP address from DrayTeK etc.
DrayTeKs do require tweaking sometimes 
Also try ENABLE IGMP Proxy and disable IGMP Snooping and reboot router and ensure the correct WAN option is selected ? WAN 1 or WAN 2 (trial and error) 
DrayTek WAN 1 and WAN 2 relate to ADSL or VDSL and WAN Ethernet connections via separate Modem connected to Router, I forget which way round DrayTeK does it
In a completely sane world, madness is the only freedom (J.G.Ballard).