A Grant of Probate cannot be achieved if there is no Will, although you can still administer the estate albeit through a slightly different process.
The rules of intestacy set out who can apply to administer the estate with a Grant of Administration. When a Will is not in place, it does not state how everything will be distributed. The administrator will distribute inheritance according to the rules of intestacy. Under these rules only the Spouses, Civil Partners, Children and other close relatives can inherit.