Tindal Street Refuge/Mission, Kings Norton

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I am trying to find information about this Refuge (? for "fallen women") that was located at 37 Tindal Street. I gather that it was taken over by the City Mission from 1886 - 1900.  The Mission did a lot of preventative and rescue work among prostitutes'
http://www.british-history.ac.uk/report.asp?compid=22981 

 I think the inmates did a lot of laundry work.

My interest is in the pre- 1886 period, specifically 1866 to the 1870s, when it was run by a William and Jemima Garner. My great grandmother was there in the 1871 census. She had had a second illegitimate birth in Oswestry House of Industry in 1866. The child, my grandfather, was still in Oswestry in the 1871. By 1881, my great grandmother was a domestic servant in Stockport, Cheshire.

Has anyone got any information on this please?

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