The lack of increase on the reading on the CT may be due to the power factor of other devices plugged in on that ring circuit be they on or in standby.
They only way to confirm would be to unplug or switch off at the wall all devices plugged into that ring circuit.
Some TV set can have quite a leading power factor when turned off but the primitive CT will not know this is apparent power rather than true power.
Then your fridge turns on which will have a poor power factor and it is possible the TV could improve the power factor of your fridge.
Thus the current the CT measures remains much the same.
BTW, the National Grid have Ring Mains, domestic homes have Ring Circuits

Automan.