hi
I would be interested in where you are with this family. I have been struggling from the other direction and trying to confirm parents of an "Elizabeth Hay" in my family and recently found that spa fields entry. Also interesting about the earlier children listing an Somer Town Address (not far from spa fields)
I Have the following info to add to the soup

in regards to what I have for MY Elizabeth Hay.
1) She is listed on census as being born in Somer Town (1851) , St Mary le Strand (1861) approx 1819, but i have various ages as ever.
2) importantly, I have a Poor Law Examination record on 20/2/1858 which has a short biography which is difficult to read. What I can see though is that she states
: Parents are John and Sarah
: Both dead by 1858, mother dies first
: Also mentions her older brother, no name
3) She deserted her family in 1862 resulting in 3 of her children spending their lives in the strand workhouse.
I am keen for any help in confirming she is your elizabeth.

cheers
Dave.