I was on a flight into London Stansted last night and about 8 minutes before landing the captain came on the PA and said something along the lines of "This is your captain, please leave your phones on flight mode, it is interfering with our radios". Then again once we had arrived at the gate he came on again with a longer message about leaving your phones on flight mode as it becomes dangerous to have interference when in busy airspace.
I've never heard a pilot request this in the middle of the flight, just at the start. What systems on the plane would be interfered with, and how serious does it get?