After saying that Wm snr didn't have a daughter named Alice, I have looked again at the 1901 census and she is listed there. I don't know how I missed her, but I did.  I think that I must agree with amondg that Alice was illegitimate and is one of the two 2 born in 1898. That all makes the Wm Britt family suggested by Rosie to be more likely, but for Wm's age being different. I need to do some research on the address given to see if that can provide any clues.
Info from the 1901 Census: 
Wm Hy Brittain     Head Mar 22     Gen Labourer Wolverhampton
Mary Ann Brittain  Wife  Mar     22                           do
Alice Brittain         Dau              2                             do
Wm Brittain          Son       6mths                             do
Ben Brittain          Bro          38      Gen Lab              do
Mary Ann (Crockett) born 1879 Wolverhampton married Wm Hy Brittain 04/1900
Thanks for the continuing interest.