Find Ancestors

Help !! I am trying to find any trace of the Johnson family within the Birmingham area. This would be my mother's side of the family tree. My mother's dad was William Johnson b.11/12/1919, and died sometime in 1992, I know his mother was called Leah Johnson, but that's all I know. My mother's mum, was Sylvia Johnson nee.Neate, b.27/2/1930, and died December 1981. She was originally from Devizes in the South West of England. Again I know her mother was called Florence Neate, who was nearly 100 years old when she died circa1996-98. William and Sylvia had six children: Patricia (now Stringer, my mother), her twin Pamela (now Leeks), Mickey, Barbara (now Forester), Jenny and Phillip. My mother and her siblings know very little about their parents history, if anyone can help me find out more then I'd be very grateful. Thanks, Scott.