Back in the days of the first LCD’s, they used to produce a lot of IR interference until they had warmed up properly. Rule this out by testing sky and amp without the TV on, or turning the backlight completely down.
IR transmitter placed correctly and has mains supply, not re-chargeable batteries.
Got any Flourescents? They create crazy amounts of interference, or used to until they changed the frequency.
I also would not keep the phone and WiFi in the same box, wireless phones also have crazy interference with WiFi, not sure if it affects IR.
Have you tried systematically turning things off to rule them out? If not, do that.