I think the Brymon Twin Otter on Birmingham-Gatwick was involved in an Air Miss west of Heathrow once, there may be an AAIB report on it.
The BMA Dash 7 was indeed an ex-London City Airways aircraft, initially in their livery but then repainted. It didn't last long. They had actually changed the branding at London City from LCY to BMA as well in the final months. They were among the last Dash-7s built.
The difficulty with such short flights into hubs is they take principally transfer passengers, where the IATA/Alliance division of fare revenue gives little return to the local connecting airline from those on through tickets. It was at the macro scale a principal reason for BMA's continual losses and eventual ending, particularly after they joined Star Alliance, and likewise why Aer Lingus actually left OneWorld. The B Cal operation to Gatwick was presumably better, just being a wet lease of Brymon's aircraft.