If no reserve executor/s is/are named in the will, the nearest relatives of the testator can apply for a 'grant of letters of administration with the will annexed' (rather than for a grant of probate). Unlike executors, administrators have no legal authority until the grant of representation has been made.
The 'pecking order', referred to by Dzug2 is as follows. (If anyone, who is entitled to apply for the grant, does not wish to do so, he/she can renounce that entitlement, so that the next person down the list then takes over that entitlement):
1. Spouse of the deceased.
2. Any child of the deceased. (Grandchildren can apply for the grant if their parent, who would have had the right to apply, is deceased).
3. Either parent of the deceased.
4. Any full brother or sister of the deceased. (Nephews and nieces can apply if their parent, who would have had the right to apply, is deceased).
5. Any half brother or sister of the deceased. (Their children can apply if they are deceased).
6. Grandparents of the deceased.
7. Aunts or uncles of the deceased. (Cousins can apply if their parent, who would have had the right to apply, is deceased).
8. Aunts and uncles of the half blood. (Their children can apply if they are deceased).
Chris