I'm sorry to hear that you're having this issue.
I don't know what would be causing your channels to move. If you're convinced that the interference in the house is causing this, then I'm not sure what to suggest, other than a separate freeview tuner.
Do you have any issues with any of the other inputs that you use?
Have just bought one of these LED TV's and am having real problems with the set up.
The issue is that the TV seems to be getting a signal from somewhere else causing it to constantly scroll through all the channels at high speed - nothing seems able to stop this.
One thought was that the infra red from the house alarm (one of the sensors is situated directly opposite the TV) could be doing this. However I've covered this up and also dismantled it to no avail. I've also tried the TV in different rooms but it still does the same thing.
The TV has been back to the shop twice and works perfectly there.
Could it be that the ariel signal is too weak and it's searching for a signal / do I need a new ariel (although it's worked well up to now and gets digital freeview channels). Could something else be interfering with it? I'm at a loss and any advice would be great.