I don't think it'll change much to be honest,
AKL is pretty full so not much room for other carriers and Air NZ already operate 5 flts into nLondon in a week so cant see that going up to any more that 7 as Air NZ don't have the fleet even with the new aircraft on order!
There also is no love lost between BA and Air NZ since they were shafted over landing slots at LHR in the days they operated out of LGW on a code share with BA....hence they joined the star alliance group.
x