She registered the birth of her son James Treadaway and signed it with a Cross, "the mark of Sarah Hoare, mother"). She gave birth and was living at 53 Wellington Street, St Luke's Middlesex.

In 1861 at the time of her marriage to James Treadaway Hoare they were living at 40 Compton Street, Clerkenwell.

Her death is difficult to spot but I am assuming it would have been registered in the St Pancras district and with her birth in 1837, this gives this possibility:

Q3 of 1875, aged 37, vol 1b, p. 112

But this death record cannot be hers in view of the divorce in 1886.
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I cannot find her birth on FreeBMD in 1837.
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Feb, 2012, TFPL: TNA has a divorce for her and J T Hoare in 1886.  Copy ordered.
TNA Ref:  J77/359/841.  She was the petitioner.

This raises the question of whether she remarried and thus had a different surname.  No identifiable remarriage can be found, though there is a good score of possibles.
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There is no way her death can be identified from the 145 Sarah Hoares born in 1837 give or take one year.