Sounds like your phone line is picking up RF interference being generated by the TV itself.
This can happen even when your router is quite a distance from the interfering kit if there are phone extensions around. ADSL filters are meant to reduce this, but you're still dealling with a phone wiring system designed the previous century. The bellwire in your phone cabling isn't needed by ADSL but is great (unwanted) antenna for interference.
I had this with a old microwave which would clobber the internet while my brothers lasagne was doing cooking. Soon as the pinger.. pinged, then the iPlayer would return to normal. Doesn't mean it was leaking microwaves, just good old fashioned RF interference.
Sounds mad, but totally repeatable (with enough lasagnes).
Could be down to the sensitivity of the ADSL chipset in the router. Moving to a Billion router from my ISP supplied one boosted my pitiful 2mb to 2.6mb.
I take it that its not Duplicate/Extend that's the problem, and it doesn't return to normal if you Only have the TV... because that would be even more bonkers.