I might be able to help here. The GWR building that you are referring to is a shed that served the Manchester Dock. Manchester Dock was (confusingly) a small dock in Liverpool built around 1785 that no longer exists.
The shed was never used by trains as such, as Manchester Dock was used by boats carrying goods across the River Mersey between the Liverpool docks and the railways in Birkenhead.
By 1872 all of Manchester Dock's quayside space had been appropriated by London and North Western Railway Co. (representing Shropshire Union Railway and Canal Co., GWR and Birkenhead Joint Lines). The dock closed in 1928 and was in-filled with spoil from the construction of the Mersey Tunnel.
I know a little bit about Liverpool's docks, but nothing about Birkenhead's rail arrangements and if anyone knows how goods were transferred from boat to train on that side of the river I'd be interested to here.