As you will need a place to talk over the days activities and tomorrow's plans, ask the mess manager if you can use the Ladies room; that is what its for. It is vastly underused and is where insurance touts, shirt salesmen etc hide at lunchtime in the fond hope that mess members will find them.
If you are all in there, shut the door and no one will find you!
If you ask the mess manager nicely (PAYD excepting) they may even bring you a tray of tea in there.