If the lady dies 'partially intestate' the niece's share remains unaffected.
The nephew's share is subject to the rules of intestacy, which means that a 'pecking order' of the right to inherit that share has to be examined. However, when it comes to the point where a brother or sister of the deceased could inherit, the children of such a brother or sister will inherit that part of the estate if their parent is dead.
Since you've indicated that the niece is the only living relative of the elderly lady, the executor will apply the 'pecking order' until the point where the deceased brother or sister (who was the father or mother of the niece) would, had he/she still been alive, have been entitled to inherit. Since that person is also deceased, the entitlement passes to his/her children which, in this case, means the niece. So the niece will actually receive all of the estate.
However it might still be best to prepare a fresh will. To do so may well mean less hassle for the executor, plus it would also (as long as the will is properly drafted) cover the situation where the niece dies before her aunt. (As it stands, the Crown would get the whole of the estate under those circumstances).
Chris