DC-ATE,
on a MD-11 for example, if you are on a 2 Engine approach and loose a second engine on short final, one of the Memory Items is to raise the flaps from 35 to 28. In my experience, changing the flaps from a intermediate approach setting to the final landing flaps, has more to do with stabilizing speed and power by increasing drag, whereas lift changes not that much.
So IMHO the BA did absolutely the right thing by raising the flaps one notch. Lift (and induced drag) would have changed relatively little - rather the parasite drag reduced.
The crew were being faced with something they were not really trained or prepared for - especially at the end of a tiring long haul flight. Everybody walked away. I have the deepest respect for the BA crew, ATC and the rescue services.
BT