To explain, the ownership of the house determines how it is treated under the rules of intestacy. If it was owned as joint tenants, each partner does not own a discrete half. It is owned by the partnership and when one of them dies, the house reverts in full to the survivor. A will or the rules of intestacy cannot alter that. If it is owned as tenants-in-common, each partner owns a discrete half. That half can either be left in a will, or, if there is no will, form part of the estate that will be distributed under the rules of intestacy.
Very basically, those rules say that if your daughter was not married (or in a civil partnership) and she has no children, her estate - including her share in the house, if owned as tenants-in-common, goes to you. Here's a flowchart if it is more complex than that:
https://www.hughjames.com/documents/docs/2020/intestacy-rules-flow-chart-february-2020-6443.pdf