Hi Josephine,
Not 100% sure, what time period are you enquiring about?
There was a workhouse there, but Blomsfield is noted on several documents.
When you say tenement?... most families in cities in England shared houses in the 1800’s they may have a few rooms in a bigger house. Let’s just say it would be good to get on with your neighbours.... no running water, no electricity, no toilet...l just an outside privy :-(