We have called this the Former County Courts Offices.  Today they are apartments but noticed the name in stone over the entrance door.  Further along there is another name for (we think) Land Registration Offices.

What we do know is it was built in 1903, thanks to a photograph taken of the Queen's Theatre (Empire Theatre) located next door, which happens to have this building surrounded in scaffolding in the background in early building stage.  The photograph can be seen at:  Flickr-1.  Another photograph shows the building in its heyday:  Flickr-2.