Black Hole
May contain traces of nut
Comparing the TV with the HDR-FOX in terms of ability to receive a poor signal is pointless, because we don't have any specifications for the HDR-FOX and I doubt you have any for your TV.Selecting the same service (Talking Pictures TV) on the TV (ie changing input from HDMI1 to Antenna) produces problem-free pictures and sound.
However: What have you done to minimise interference between the outgoing HDMI and the incoming signal? Does the PQ improve if you touch the aerial plug?
Try using the V-FORMAT button to switch HDMI output to 576i and see if that changes anything. If it does, you might want to improve the separation of the HDMI and aerial leads, and/or use higher quality screened cables. Changing your customary format from 1080p to 1080i might also solve the issue without apparent degradation of the picture.