If your wheel-well looks like Nich's photo above, then it appears that you still have the original MGR ICE. The bits which can, and do, whir and buzz even when not "in use", are the the TV tuner/video and radio in there. Also, a bit higher up in the rear wing, the combined SatNav unit/ CD-Player (the CD-Changer in the well, only when in use).
All the whiring and buzzing should however stop within a couple of minutes after everything is shut down, locked or unlocked. As much as opening or closing a door will be enough to set them off again though! It's not a problem, unless one of them decides not to obey the 'switch off' signal sent shortly after shut down. That is not uncommon, often as a result of water ingress into the battery-well damaging one or more of those units. Many complete ICE systems have been changed from the MGR original for that very reason I believe, rather than a desire for better quality sound.
... so, just leave the car totally untouched for five minutes and go listen again!