Assuming this is England and Wales:
I think that what happens if someone dies intestate the next-of-kin applies for a Letter of Administration (from a Solicitor??)
The Grant (or Letters) of Administration are issued by the Probate Office. A lot of people make their application with the help of a solicitor, though this isn't essential. However, if there isn't a will, administering the estate would involve tracking down all entitled relatives, and not everyone feels up to doing that themselves.
This Letter of Administration permits the next-of-kin to distribute the persons monies etc.
(I guess that usually the next-of-kin would be the closest relative and therefore the main beneficiary.)
Or possibly one of the main beneficiaries - if there were several relatives who were equally closely related, such as a set of siblings, it might be that one of them applied for Administration, but they would each get an equal share.
In this case the deceased was an only child, never had any children and both her parents were dead so any relative is a distant one. I called her 'aunt' but in fact she was a second cousin to my mother. I think there will be many distant relatives like myself.
In England and Wales, a second cousin doesn't inherit in intestacy cases. Entitlement goes as far as first cousins, plus their descendants. (I believe the net spreads wider in Scotland.)
Not after her money - curious to know who sorted out her estate - honest!
The only way to find that out would be to order a copy of the grant. It should say who it was issued to - worth a try at £1.50?