Have you joined Genes Reunited?
http://www.genesreunited.co.uk It's very difficult when you don't have much information to start you off, maybe you'll find your Father's name has already been added by another relative - it's worth a try and free to search, although you will have to pay a small yearly subscription if you want to contact other members. When you have your Father's birth certificate you should then be able to trace his parents' marriage on FreeBMD
http://www.freebmd.org.uk/ and apply for the certificate online at
http://www.gro.gov.uk/gro/content/ (which covers England and Wales). This certificate will give you your Grandfathers' names and professions and hopefully a starting point for searching the census. Ancestry is really good and I think they are still offering a free 14 day trial
http://www.ancestry.co.uk/