Hi Arthurs
Welcome to Rootschat. If you know the date of birth of your father, you could buy a copy of his birth certificate, that would give you his father's name.
Or you could search the 1901 census for your father and find him and his family, which would give you his parents (your grandparents) names. If you search FreeBMD.org.uk you will be able to find your grandparents marriage. If you send off for that certificate, you will then find out the name of your g.grandfather. Or just keep searching through the censuses back to 1841 to find ancestors and with a bit of luck you will find out about siblings etc. Of course, you will in the end need to buy certificates to verify the information you have found. Then, of course, there is your mother's family to research too. The further back you go, the more ancestors you will find.
If you want any more help, or questions answered just ask. Many of the Rootschatters are far more experienced than I am and between them usually come up with an answer.
Liz