The B737-600 (Flap/leading edge modified), IS approved for LCY ops, but BA have chosen Airbus for the Shorthaul Operation / 'Special Services' to keep costs down and commonality accross the fleet.
It will be interesting to see who ops this acft for BA (ie BA Mainline or BACityflyer etc etc...) There are 'recency' issuses with LCY as crew have to keep current with approaches and departures but with zillions of BA Mainline airbus crew, its would be impossible for them all to be current.
It would be great for BACityflyer as the Airbus would be a welcome addition by pax, crew and staff all round. It could operate south from Scotland, then over the pond. Would need more that 2 though...