We've already got an H24 A/G service. It's called London/Scottish Information. They should be able to provide you with similar information to field based A/G operators.
The main issue I can see with remote ops is the airfield authority permitting the control and use of its airfield, remembering that not all airports are controlled by NATS. I fail to believe anyone will entrust their multi-million £ infrastructure to an A/G or FISO. In essence I suppose it could work VFR only, but for such a small gain it becomes implausible.
Furthermore, reasons for airports closing at night range from little revenue generating traffic, airport manning including ATC, RFFS, baggage handlers, etc, noise abatement, emergency diversion availability, the list goes on.