The test gave the right answer - InProc was setup correctly.
However, your first post regarding generic handlers got me thinking.
Whilst the problem was manifesting in the UserControl in question this control was being loaded into a Composite page.
So, in the file CompositeC1Page.cs in the Core library it was necessary to add ", System.Web.SessionState.IRequiresSessionState" as an inheritance clause.
Immediately this was added and I ran my project Session was no longer null :)