Garden light connected to main lounge light stopped working
You mentioned the outdoor light is on a sensor, which means it just needs a constant supply of power and handles switching itself. If this cable hanging down is in fact the supply to the outdoor light then connect the blue cable into one of the far left block of 3 (that also has an existing blue cable connected) and the brown into the central blocks (in your picture it has 2 brown connections). In a ceiling rose the two blocks of 3 are the constant supply and the single block of 2 is for the switched supply. So you will effectively be providing a constant supply to wherever this cable is going.

If the garden light still doesn't work then unplug it and get someone in, it may have been unplugged for a reason!