'Next of kin' has no meaning in law (or certainly not a universal one anyway). If you're going into hospital, for example, you can name anyone as your 'next of kin'; they don't have to be related to you. Such an unrelated person would have no right to any part of your estate if you were to die intestate (i.e. without leaving a will). A related person would only receive part (or all) of your estate if that's what the intestacy rules say should happen anyway. (i.e. being 'down as next of kin' is completely irrelevant).
The flowchart in Ubasses' link explains the law on intestacy or you can use this link:
https://www.gov.uk/inherits-someone-dies-without-will