If your father left the house and substantial assets (over £20,000) then you are going to need to apply to the Probate Registry for Letters of administration. The government have produced a few webpages which will guide you through the process. If you follow this link it will take you to the government website pages.
If there is no will then the estate passes under the rules of intestacy. If your mother is no longer alive then the estate passes in total to you.
That is a standard formality. Once you have the grant of probate/letters of administration, that is the authority that you will need to transfer the house, bank account contents and other assets into your name.
If you feel competent, there is is no reason why you cannot do this yourself or you can always instruct a solicitor to deal with the application for you. It is a relatively straightforward process but, if solicitors are not doing it for you, you will be required to attend an interview at the Probate Registry.
Can I clarify anything for you?