Can't speak to UK hospitals or buildings in general, but in USA, at least in FL, a much more common problem is oversizing rather than undersizing AC systems for the load.
Doing so greatly reduces the ability of the system to control humidity, which, regardless of what this article implies, is much more important to the health of the occupants (and the building itself) than the temperature.
BTW, in any large building, opening windows around the perimeter will do little or nothing to control temperatures in the center of the building.
You do not want the windows open for several reasons. Safety is one. And it is called Air Conditioning for a reason. Ozone levels in a city are an issue and cause issues for patients with compromised breathing. You want the air filtered as much as possible and the proper humidity maintained to lessen encouragement of unwanted bacteria etc.
Any maintenance man can walk up to their chiller and make it operate at reduced capacity as if the building were under capacity. The way you'll know if you are cooling too much when using multi chillers is simple. The will be running at low capacity or cycling on low chill water temp.