I don't have access to the birth records, but do have access to census records through ancestry.com.
I have located the Hickson family in the 1891 census in the civil parish of Stratford le Bow (sub-registration district Bow of registration district Poplar), Middlesex County, with husband Henry (age 36, bootmaker, born Shoreditch), wife Fanny (age 33, mangler, born Bow), and children Mary A (age 7), Emily (age 6), Alice (age 4), and Eliza (age 1), all children also born in Bow.
The 1881 census has Fanny born in Mile End, which is also in the East End of London.
Thus, of the three choices for Fanny Burrell you have in her profile, it is definitely the first one (birth registered in Mile End, Middlesex)