It’s mainly due to the extremely large tail fin, even when compared to the 747.
At LHR, the CAT III holds are 137m from the runway centreline, and this provides sufficient protection for the localiser signals. This is the Localiser Sensitive Area.
An A380 has a more marked effect on the localiser. It is fine if it is facing towards the runway while holding at the CAT III, i.e. as if to cross the runway. However, if it is in the same physical position (just clear of the CAT III hold), but facing away from the runway (so the tail fin is nearer the runway), the fluctuations are outside CAT III tolerances. Hence, in some areas, the A380 has to be 192m from the runway centreline.
There is also a similar effect on the localiser if an A380 rolls to the end of a runway, depending on how close the localiser is to the end of the runway. In some ways this can be worse, depending on the length of the runway, because this might well take the fluctuations outside of CAT I tolerances.