TBH I doubt it is quite that simple, because the OP is asking specifically about what he perceives as a
recent increase in diversions.
There may well be a minor 380 factor but don’t forget though that when 744’s were first delivered to BA, starting in ‘89, they served the same routes as currently served by BA’s 380’s, and actually weren’t that much lighter on capacity ...AFAIR it the original BA fit was >400 seats (? 409 from memory). Now whilst I’m well aware 744 capacity has reduced over the years the point is the 380’s certainly aren’t carrying an order of magnitude of pax more than older BA types and are only going to the same destinations and on the same routes as BA has operated on for years...
If there’s been a recent short “spike” in medical diversions at BA then from what I am aware of (or not) it is a v small one..some of it might be blamed on the 380 but in all honesty it’s more likely down to randomness, plus as others have said time of year (bugs, demographics of those travelling).
This open source but generally reliable website might be of interest:
http://thebasource.com/tag/medical-diversions/