Hi Cassie, it is a little hard to help based on the information that you have given, since you first posted you have found that there is a George Frederick LEEDHAM.I think this is the one you were talking about.This is the birth registration.
Name: George Frederick Leedham Year of Registration: 1890 Quarter of Registration: Jan-Feb-Mar District: Nuneaton County: Leicestershire, Warwickshire Volume: 6d Page: 471
I also found this one, which is a little later, still in Warwickshire.
Births Jun 1905 Leedham George Frederick Birmingham6d 2
What I suggest you do, is get as much of the verbal information from your parents as possible.If they know anything. Though I am sure you have done this.If they are really not too sure, you are best to get the relevant birth, marriage or and death certificates, that apply. Starting with your parents, birth certificates.If they can give you ALL the info, then move to the next generation.
I have plenty of LEEDHAM info as I am sure many others do, but unfortunately, in this instance I do not have the later generations that apply to your family. I may be able to help with some of the earlier generations.So keep in touch.
An estimate of dates is very helpful. I have tried to have to do a bit of a search but without any hint of time, it does make it difficult.