Not sure about the E53, but it's not uncommon for manufacturers to run the left and right side lighting on different circuits and fuses so one blown fuse doesn't mean you lose the lot, just that side.
This
piccie is the front fuse card, but no fog lights marked on it from what I can see....but it is a US card as I haven't found a UK one so far.
Nor does it seem to be on the
rear board either...
