Assumptions make an ass out of you and me. That wouldn't even be the biggest waste of resources I heard about this week.
Having said that, it's certainly possible/feasible that the tunnels are being used. The case against would be that these tunnels are in very sensitive areas, and so the security restrictions on any potential use would be very strict.
The Whitehall tunnels also provide a handy way to avoid the rain and the public while walking between departments.
So far as anyone knows, there are no permanently manned offices down there, although there may be some storage.
(Obviously I'm not counting the alien base under Buckingham Palace, because that's Beyond Top Secret, as everyone knows.)