Her spouse (your Dad) is the first person on the "order of entitlement" to extract a Grant of Administration. This is the legal document which must be obtained to transfer the assets of a person who dies intestate (without a will). This document is issued by the High Court, on completion of certain formalities - including payment of any taxes and duties, if they arise.
With no will, your Dad is entltled to 2/3 of the estate and their children share 1/3. If there were predeceased children (your brothers, sisters), their share may be divided among their children (your nieces, nephews) "per stirpes".
If, however, your mum had no other assets apart from the house, then your Dad may have certain rights to retain the property in full, since it is the "family home".
Need to employ a solicitor