Have just had another look through Gore's directory and it looks like my Gr Gr Grandfather started using 32 London road around 1868. If the current building dates roughly to 1870-1900, that's on the edge, or just outside, that timeframe...
Also had a look at the history of the Liverpool Blind School, there's some info here:
https://historyof.place/location/liverpool-school-for-the-indigent-blindIt says that the school in London road was definitely demolished in 1851 and moved to Harman street. The town plan from 1848 (revised 1864) still shows the school in its old location: am wondering if when the map was revised only parts of it were revised?
Anyway, presumably when the school was demolished in 1851 another building (predecessor of the current one) was put up. Assuming the warehouse was brand new when my Gr Gr Grandfather moved in around 1868/69, that 1851 building would have been demolished after only about 17 years - unlikely perhaps?
So I'm thinking maybe the current building dates from the 1880s or thereabouts, meaning it was not my Gr Gr Grandfather's warehouse, but who knows...