It still does in the form of Airport Co-ordination Ltd. They have a good website
Airport Coordination Limited - Welcome to ACL which has statistics which show available and used movements per hour (basically the same). Just to think when T4 was opened the agreement was to limit ATMs to, I think from memory, 265,000. That didn't last long!
Mind you in those days sector times were much shorter than they are today - 60 minutes in each direction for AMS & CDG. I wonder how much extra the longer block times cost airlines in fuel, crew, additional aircraft and so on. Still the airlines must have thought it worthwhile whilst agreeing to higher hourly limits. Indeed the likes of VS really owe their slot holdings to the increase in movements that has occurred.
Actually in my experience the problem is isn't so much holding waiting to land as waiting to take off, but aircraft stil burn fuel whilst taxiing.