I have found this family which I think is the one you are looking for:
1851
Half Island House, Firbank, Kirkby Lonsdale
William Bateman, 48, blacksmith, born Lancs, Cartmel
Mary, 46, Westmorland, New Hutton
Mary, dau, 25, servant at home, Firbank
Miles, son,21, blacksmith
James, 18, " app.
John, 16 "
Betty, 10
Eleanor, 6
William, 2 grandson
Richard Greenbank, lodger
Thomas Greenbank "
Willm " "
All the children born Firbank
This looks like Miles the father of your William so in later censuses, we should be able to find him by his place of birth.
Jen