The rules are explained here
https://www.gov.uk/inherits-someone-dies-without-will
or in this flow chart:
http://www.emgsolicitors.com/wp-content/uploads/2016/11/rules-of-intestacy-flowchart.png
(You might need to enlarge the image,by pressing Ctrl and + together a few times if you're using a Windows computer, to view the text there)
When someone dies intestate there is a 'pecking order' defining who can apply for a 'grant of representation' (in the form of 'letters of administration') empowering them to distribute the estate of the deceased person in accordance with the rules. In practice that generally means that the person who is nearest to the top of the flowchart in my second link (or one of several people if, say, the estate was to be shared among siblings) is entitled to apply for the grant.