I am aware of this:
However, this only gives you the borders for, for example, 'L' rather than:
L1, L10, L11, L12 etc.
Can I obtain these fine grained border data from somewhere free? Thanks.
Take a look at this site: UK Postcodes
It has the CSV data for all the boundaries. You can also download a KML file at each level to display in Google Earth, or QGIS where you can do more analysis.
Unfortunately you may need to individually download each Area to get detail for the next level down.