A Grade II* building The Tower was built in 1908 as an office block; it was converted to apartments in 2006. The architect was W. Aubrey Thomas, the same man that designed the Royal Liver Building.
This is actually the third “tower” to have been built on the site, with the first dating back to around 1406. During the 18th century the so-called Tower of Liverpool was a jail which housed, amongst others, prisoners of war during the Seven Years War.
By 1819 the jail no longer held prisoners and was pulled down and replaced by warehouses. A second tower was built in the 20th century but then demolished to make way for the present building.
You can find some more photos here.