Under the intestacy rules, the whole of deceased person's estate (including the house) would pass to the Crown:
http://www.wrighthassall.co.uk/media/article/attachments/Intestacy_flowchart_after_1.10.14_5_Aug_14.pdf
However if the deceased person had been living with someone as if they were their spouse (for a period of at least 2 years immediately prior to the death occurring) that person could apply to a court to have the intestacy rules varied in order to 'make reasonable financial provision' for them.
Similarly any other non-relative. who was being maintained by the deceased person up until the time of their death, could apply for a variation of the intestacy rules, as could anyone (such as a step-child) who had been treated as a child of the deceased person during any marriage that the deceased person may have entered into.
In all of those circumstance it would up to the court to decide whether the claimant had any right to receive 'reasonable financial provision'.
http://www.legislation.gov.uk/ukpga/1975/63