Hi
I have Hart in my tree, the only Annie I have found was my grandfather's youngest sister b 1900. I do not know any details about her. That is not to say that there is not another Frances Annie in the next generation as I have only found 3 siblings and the Harts were of Irish descent!! Interestingly my late uncle was christened Francis Hart.
There is one birth in Q4 (Dec) 1913 of a Benjamin Tregay (Hart mother) Birmingham 6d 399, unfortunately he did not live long and died in Aston Q2 1914 6d 653.
Best wishes Sue