According to thebasource(dot)com:
CityFlyer E170 Operates from LGW (11th August 2012)
BA CityFlyer Embraer E170 G-LCYF positioned London City – London Gatwick last night as BA9252 and operated the BA2902/BA2903, BA2906/BA2907 and BA2908/BA2909 London Gatwick – Manchester rotations today.
Seems it can be done - as mentioned above they will classify it as a charter to please the unions. For the general public, they'll be none the wiser as all staff will be in BA uniform in a BA liveried aircraft (dare I say nicer than the 737!).
Still, it rarely happens and Titan must be making a mint from BA at the moment. They seem to have at least one aircraft (sometimes 2) permanently stationed at LGW operating for BA recently.