"a closed airfield is like a closed retail store, garage, theatre. It means that it is not accessible without specific negotiation with the owner."
NO. A "closed airfield" in the uk means whatever the operator wants it to. It is common for an airfield to be closed - no fuel, no food, no maintenance, no office to pay landing fee, but you can fly with prior permission. All a pilot has to do is check what the operator had in mind by using the word closed, not a big issue.
Rod1