Interesting. This kind of thing has happened in many cities.
I think it is often true that the girls school does later decline for the reasons mentioned by other posters....some girls want to move to co ed to 6th form, raising the standards of the co ed and reducing them in the girls school.....then parents choose the school with better results from lower down.
This is not always the pattern, especially in boarding schools which are a special case. In day schools though, there is a trend of decline in numbers in girls schools anyway, as more and more people prefer co ed. There will always be a place for girls schools, but it is more of a niche market these days. This trend is speeded up by boys schools going co ed. the decline of girls schools can take many many years though.
Where I live, the boys school went fully co ed almost 20 years ago. The girls school in the town (which had no formal links or reciprocal arrangements) has been in slow decline for many many years in terms of numbers. There are many reasons for this, but one was the fact that some of the girls who would have gone there, went to the co ed school instead. This year, possible closure of the girls school was announced. It has been saved, but only by going co ed itself. There simply wasn't the demand for a girls only school.
Places that have highly successful girls day schools tend to have boys schools close by. Or they are richly endowed, so can attract the very bright with generous bursaries, to keep grades up, which isa big selling point for other parents. It is almost always the boys schools that go co ed (more flexible as not in girls school organisations) perhaps because even fewer parents are committed to boys only ed than girls only ed. The girls school then bravely says they are continuing to provide single sex ed, as that is their selling point and girls do better in single sex ed......but given a few years, start to struggle and then (generalising here) often become the school for girls who cannot get into the co ed, or who for other reasons don't want to be in a mixed environment.
It is a shame for the Girls School in Nottingham, because whilst what I mention above is not inevitable, the boys school going co ed will certainly make the future of the girls school more difficult. On a very basic note, the parents of girls now have more choices than before and some will opt for the new option which was not there before. If the girls school does not have the funds to offer bursaries to make them more attractive than the competition, their position in the long term is not enviable.