This is an illustration from 1826.

A map from around 1700 shows the tower with the buildings front and rear too. The buildings look pretty contemporary to the 15th century, but the tower would've have been free standing when built. How soon the houses were built either side is anyone's guess, short of a detailed search of public records. Medieval townsfolk were little different in their attitudes to property than we are, so I'd be willing to guess that the buildings were up not long after the tower was completed.
I don't know how big an area you're covering, but the Abbey was walled and gated from the town in this period, the tower itself being built as a show of pride by the good burghers of the town against the Abbot.