I just thought I'd write something here, as everyone else seems to have no interest in sharing their experience here.
The group exercise consisted of a 50 minute session, 40 of which are dedicated to preparing a presentation and the remainder for the presentation itself.
The group is given a whole load of unfiltered information about a random topic, and is asked to come up with a short (3-4 min.) presentation introducing the topic (in this case, a public health problem), the nature and scale of the problem and then think up some possible practical solutions to it.
The presentation, the title of which you are given in advance, is purposely broad in nature. The people watching the presentations don't want to see the same thing over and over, so they encourage you to go wherever your heart takes you with this. I think as long as it's relevant, concise and has some interesting talking points, the presentation skills are probably the main thing rather than the content.
Finally, the cases you are given are not really like standard consultancy cases, in that there isn't really a need for a framework or anything like that. It's just about finding where the problem is with some fairly direct questions, and then some mental arithmetic.
All in all, quite a pleasant interview day; everyone at the company was very friendly throughout.