I have to create a catchment area (based on LSOA) for the 19 underground stations within Camden borough and it has to be in a polygon vector file. I know I have to somehow group the SOAs but don’t know which geoprocessing tool to use.
This can be calculated quite easily using Voronoi Diagrams (also known as Theissen polygons) based on Euclidean Distance metrics (i.e. "As the crow flies") in GRASS, QGIS, or ArcGIS. In all three of these platforms, the linked tools take as input a point feature class and output a polygon feature class.
If you are trying to calculate based on travel time (i.e. drive time), the problem becomes more difficult. See this link for more information if that is your case.