What problems are you having exactly?
The BA mobile website and BA full website work perfectly on my iPhone (iOS 7) and iPad (iOS 6). Search, BAEC login, bookings, etc. Some dynamic elements such as the calendar popup take a few seconds to work.
IOS 5 and 6: Calendar pop ups won't work at all, for me. (The drop down calendars won't engage -- i have to enter dates manually.). Displays are wonky and text hovers over other text -- even though I work in landscape view almost exclusively, the displays never fully resolve into discrete areas and cross over each other. Continued demands to re-login, when moving around the site -- but that happened when using IE, so not new.
Can't buy in that site is improved when it's less useful and less stable, now.
Again, I'm using the US site, so YMMV.