This Wikimedia article goes a bit further into it: The blue plaque on the side of this rather nice looking pub says:
Charlotte Bronte (1816 - 1855). In 1846 The Revd. Patrick Bronte came to Manchester for a cataract operation accompanied by his daughter Charlotte. They took lodgings at 59 Boundary Street West (formerly known as 83 Mount Pleasant). It was here that Charlotte began to write her first successful novel Jane Eyre.
So, ambiguous info from Manchester's Blue Plaque people (who are presumably bigging up Manchester's tourist opportunities), but clearly it wasn't this building, which I'd say dates from the 1880s?
The problem is that the plaque was first placed on a building in Boundary Lane some distance to the west. When this building was demolished for redevelopment the plaque was saved. The Brontes were lodging at 83 Mount Pleasant and the eye hospital was then in South Parade, Manchester (until 1867)
The building, as per the Manchester Evening News article, however, does date from the 1840s, not the 1880s. bronteblog