If the person died intestate (ie without a will), the following people are entitled in this order to take out the Grant of Representation and deal with the estate:-
The surviving husband or wife
the children of the deceased and the issue of any deceased child who died before the deceased
the father and mother of the deceased
brothers and sisters of the whole blood and the issue of any deceased sibling of the whole blood who died before the deceased
brothers and sisters of the half blood and the issue of any deceased sibling of the half blood who predeceased the deceased
the list then continues.
Each category has to be "cleared off" (ie it has to be established that there is no one surviving in a category who would take a beneficial interest) before you move onto the next category. There is no preference for age and basically the first to apply can take the Grant. however, this does mean that the eldest sibling MUST apply - they may decide not to bother.
If the deceased left a will but did not appoint an executor, the rules are different. The order of priority is:
1 residuary beneficiary or trustee of a a residuary share
2 residuary beneficiary (incl life tenant) incl those under partial intestacy (ie where some of the estate is not properly disposed of)
3 the personal rep of category 2
4 the personal rep of category 3
5 any other legatee or creditor
6 the personal rep of category 5