Bringing BA's operations into line with the no-frills airlines does not mean that BA is either going to launch another spin-off airline, or that they are planning to turn their economy class product the same way that EI has.
Indeed, if they were planning to follow EI's lead, I would suggest it was from an operational point of view. Like how can BA get the most out of its aircraft, crews and ground operations. As I mentioned, I don't think this will lead to an airline-within-airline as Mr. Eddington is much against the idea, and also BA would not be stupid enough to provide a no-frills service in Euro Traveller. Their advertising campaign for shorthaul has been focuses around full service for no-frills prices.
I do know CitiExpress is looking at a makeover to make it more inline with the LCCs (I heard one family of aircraft and no more Club Europe, with the before mentioned fast turns etc.) but cannot comment.