Hello again Sue R,
I doubt you'll be able to do too much (if any) "cross-referencing". If Gma Annie was very young when she had a child in 1920, she might well have been born after the 1901 census so that would leave only the 1911 census in which to find her ... And then, how would you know she was the right Annie? Unless she was living at the address given on your mother's bc.
There are only three possible births of an Annie ARNOLD in Tamworth (though we don't even know whether that is where your grandmother was born) on FreeBMD. An Annie in 1897, and an Annie Irene and an Annie Elizabeth in 1904. There are no matching deaths on FreeBMD up to 1920.
Just for information, the 1897 Annie seems to be the Annie aged 3, born Glascote (part of Tamworth - mistranscribed as Glascoed on Ancestry), daughter of Harold and Sarah ARNOLD, living in Aston.
Reference is: RG13/ 2865/ 54/ 17
Regards,
JAP