If its not the HDMI cable there are a couple of possibilities: most likely there is an issue with the tv box picking up the broadband connection effecting how the live TV channels are being received. If not already I would do a full power down of your broadband hub and the openreach white ONT (If you are full fibre) for at least 2 minutes and power all back up and that may help.
Failing that I would call the technical help team who will I'm sure be able to see whats what and advise on any other steps - I had this once and they had me do a few different steps in a certain order (I can't remember them all now) but got it working
