Hartington.... Running a stack, or stacks (Heathrow has four) is a routine task. When one is taken off the bottom, the others are laddered down. The controller can either use an aircraft report that it has left a level before clearing the next one down, or he can use SSR to see when the levels are clear. It's fairly common to take aircraft out of the stack "out of turn" to provide the best landing rate when wake turbulence separation is a consideration. E.g if there are 4 heavies arriving at similar times, they may be sequenced together to avoid big spaces with lighter aircraft between them. Equally, 4 or 5 medium aircraft may be taken off together at the expense of 1 or 2 heavies which are already there. It's basically "first come first served" but ATC also has to achieve the maximum landing rate consistently.
Nicholas49.... Aircraft routeing into the holding stacks work a number controllers from the time they join UK airspace. However, once they join the holding patterns they are (usually) under the control of the airfield approach sectors. Heathrow has four holding patterns. Two to the north (BNN and LAM) are controlled by the Intermediate Director (North) and the two to the south (OCK and BIG) by the Int Dir (South). If things get very busy, each can call for assistance by a further controller who then takes on the task of accepting inbound releases and descending aircraft in the stacks on the same frequency as the radar controller. The Intermediate Directors take the aircraft off the stacks, direct them into a circuit for landing and start their descent. All traffic from the 4 stacks is then landed to a Final Director who's task is to direct them on to the ILS providing the required spacing before handing them to the Tower.
Aircraft in the holding patterns are on their own navigation so they fly the patterns without radar assistance. It's usually done by the autopilot.
If an aircraft wishes to maintain altitude, those above must maintain theirs. It would be possible, using radar separation, to descend other aircraft through the one maintaining its level but it's not something I ever recall seeing.
Phewwww.. HTH.