First thing is that "felony" doesn't directly translate into UK law. They have different concepts.
As people stated here, Garry's information is pretty good. So read it.
I did something stupid and have a "record" myself, but I got two years probation and when I applied for my civil partner visa, they barely gave it notice.
The problem is that they try to translate what you did into UK terms and if that crime would have ended up with > 12 months of prison time, then they are unlikely to automatically grant a visa. But as Garry's information states, family have right of appeal. They let Mike Tyson in who spent several years in jail for his stupidity. So it isn't a "never" thing. It is just might be a difficult road.
Also, certain crime are considered spent in the UK after a certain amount of time after you have finished being punished for them and then you are under no obligation to report them (except as Gary points out in one of the posts, they are "crimes of dishonesty" or other certain categories). So a lot of it depends on what your father got convicted of, what his sentance was and how long ago it was. If you are willing to share some of the details, though I know that is personal, we might be able to help figure out if you are in for a short battle or a long battle.