MV has provided an accurate answer but it might not actually help you work out who 'the next person entitled . . . ' actually is.
This is quoted from 'Wills & Probate', published by the
Consumers' Association:
"The nearest relatives, in a fixed order, are entitled to apply for the grant. If the nearest relation does not wish to apply, he can renounce his right to do so, in which case the next-nearest becomes entitled to be the administrator, and so on, down the line of kinship"
The following is a summary of the list (in order) which follows that paragraph:
1. The surviving spouse, if any.
2. Any of the deceased person's children. (If a child of the deceased person has also died, any grandchildren, through that child, may also apply at this stage).
3. The parents of the deceased person.
4. The brothers and sisters of the deceased. (Also the children of a brother or sister).
5. Half-brothers or half-sister, or their children.
6. Grandparents of the deceased person.
7. Uncles and aunts (excluding those by marriage), or their children.
That completes the list. No other person is legally regarded as 'next of kin'.
Hoping that makes some sort of sense,
Chris