I think when granddaughte referred to Probate she meant the process of obtaining the Grant of Letters of Administration (which is colloquially known as Probate, since it is dealt with by the Probate Registry).
Whilst there may be no close relatives, there may well be more distant relatives who would take the estate under intestacy rules. If not, it will vest in the Crown as bona vacantia and in my experience, they will not make provision for anyone.
The best bet is for the poster to take urgent legal advice with a view to making a claim under the Inheritance (Provision and Family and Dependents) Act 1975, either as a cohabitee or as a person who immediately before the deceased's death was being maintained by the deceased. The claim is one for reasonable financial provision and should be made within 6 months of the Grant of Representation being extracted. Public legal funding may be available in certain circumstances so it would be worth investigating. I have actually done these on a no win no fee basis. I would suggest trying a solicitor with a free half hour interview and take it from there.