Thread updated from 2012..............
You probably have exhausted every avenue looking for the birth records of Thomas and Annie - this was a note on the Berglund Family tree info :-
1885 - Not marriage; "relationship" btwn 1885-1889 (when Thomas + Annie Yarrow conceived/born). Henry, widow of Mary Henderson Todd (she died btwn 1871-1881 censuses). Mary was Jane's sister. Jane (+ her kids) lived with Thomas, while married to Edward Bell.
Tree Notes that Jane Todd born 1844 Morton/Murton Northumberland died in 1907 Salford Lancashire. Buried in the same grave as her daughter Emma Bell born 1873 who died in 1927.
Sandra