My first thought was that the iPad is too large for this. A smaller 7" tablet would be easier to carry in one hand or in an apron pocket.
My second thought was that even that's too large and gets in the way. Will they have iPad stands on top of the serving carts? That would work. Or they could use iPads while in the galley, and...
I really don't see an issue here. Most airline uniforms I've seen have an included jacket for colder climates they go into. They would , I imagine hang these up out of the way when not in use. Just store them in the lining of the jackets.
A very simple and cheap alteration could be made to secure the iPad in their uniform jacket so it doesn't fly out of the coat on take off
I also don't think they would need to have one per flight attendant. Maybe five per flight.
You have your front and back galleys that would probably need two each so the attendants can quickly update passenger info on both sides of the plane and also having a main plus one reserve. Plus one in the cockpit for the pilots if they need it (if that's at all possible)
Or at the very least one each for front and back galley so they can instantly update each other with things to grab for passengers or about passengers needing special attention (e.g. Mary in Seat 7G need a extra blanket for her 5 month old , front galley near her doesn't have the right ones needed so polls the back galley to bring it down. etc etc)
I don't see them carting them around the aisles for the entire flight - they will be referred to as a business tools then stored away when not in use. During take off and landing flight attendants already go around getting passengers to secure things and I imagine they would secure things themselves - the iPads could just be another one of those things they have to strap to something. There's usually enough free locker space with included straps in airline galleys AFAIK.
For moving about the cabin, they should have a more subtle wrist computer that reads out info as the attendant passes each passenger row. A quick glance while talking or serving would give personal info and preferences / orders.
Which would require more development time while an appropriate device is either fabricated or suitable piece of hardware is sourced & licensed.
BA would have system analysts working for them that probably did look into the development cost of creating their own device and decided to go the easier route of sourcing iPads.
If anything it means they get to type into the advantages developing for the iOS brings. A vibrant development community. Supported by Apple for future system updates. Both of which means less work for overstressed developers working for them. No hardware research costs. If anything goes wrong they can use Apple Care / corporate equivalent for tech support.
Let's be honest here - some of those flight attendants are going to be playing games on those iPads. Make it a job performance related perk ie if your performance goes above a certain level for x months you own the iPad. In a competitive job market an airline needs _every_ advantage it can take.
It has a high turn over of rewards and benefits for a lower investment cost then developing their own hardware is.
Lastly if this Enterprise app of these takes off guess what! Depending on the terms of the Enterprise program they could possibly sell the software solution off to other Airlines. The advantage of doing it first means if their program is successful they could possibly sell it off to other airlines. With good luck this investment of theirs could pay for itself !