It's all well and good moaning about the CAA, except it is misguided in this case as it has not been necessary to use a licensed airfield for PPL training since 2010!
If an airfield is closed, it's closed. Simple as that - it has nothing to do with the licensing state. It's private property and they've decided you don't want you there - so tough!
Unlicensed / Licensed only affects public transport flights and is irrelevant in this context.
-edit- crossed with GtE