Hi
I know the area very well and was born in Withington Hospital, my grandparents lived on Nell Lane too. I feel there isn't a really good explanation anywhere on the internet re Withington Hospital, Withington workhouse and 20 Nell Lane. Having done quite a lot of research on my family and extended relatives families too, I have found that there are 2 people in my tree that died at 20 Nell Lane. Neither were related to each other at all, dying 10 years apart there, one being a great uncle of mine, the other being an uncle of a cousins husband. So no relation at all.
I know that Withington Hospital was formerly the Workhouse, but 20 Nell Lane is the opposite end of the Lane to the hospital/workhouse. I think, especially having obtained death certificates for those that died and so seen what they died from, that 20 Nell Lane was some kind of hospice, connected to the Hospital about a mile away.