The City Arms occupies a former 18th Century town house.  The Vine Inn occupies two buildings.  The first is also an 18th Century town house, with a row of windows on the upper floor that resemble those in a weaver's cottage.  The pub extends into the building next door, that was once an office/warehouse building.  A map from 1886 (my version of it is shown below) shows that by then the houses had already been converted into public houses.