THIS WORKED FOR ME - IT IS YOUR MOBILE PHONE
I had the same issue. All BBC transponder signals froze the TV. It was intermittent, but usually occurred within a very short time. Resetting/Re-Tuning did not cure it. The only way to access the TV's functions again was to power off and on.
I initially assumed it was too much signal, but it was not that either.
It was as if something was causing the TV to have an internal mental breakdown but only on the BBC transponder channels.
I was about to give up, and send the TV to the tip, when I found the solution by chance.
I had started to use a TV card in my PC, because of the problem, but there were often occasional wavy lines, and buzzing on the sound. I knew from experience this was due to a mobile phone doing its periodic background 'check in', and of course when it was transmitting during a conversation.
So I bought a TV aerial filter designed to limit mobile phone frequencies, and fitted it between the aerial and the aerial amplifier I use to distribute the TV signal, including the feed to the 'poorly TV'.
These filters are described as being designed to limit 4G interference, but they actually limit 3G frequencies as well.
THAT WAS IT.
The TV started working with no problems.
I checked several times. Remove the filter, and the problem returned immediately. Connect it, cured.
So, strange as it sounds, some Digital TV's must have a control chip that reacts to 3G and 4G nearby interference, which causes that one frequency band to 'freeze' the normal operation when the mobile transmits. As you may be aware a mobile phone transmits in the background often, not just when you are making a call.
A VERY peculiar, and almost insolvable problem with a very EASY cure.
There is a distinct possibility that fitting a filter may cure a lot of problems people are experiencing with the BBC channels, not just the one above. Fitting could not be simpler, TV aerial plug at one end, a socket for your present aerial cable on the other. The filter requires no power. For the best result, fit the filter directly to the TV's aerial input socket.
Marlbrook, October 2014