Isn't the main issue the time/inconvenience here? It will take you an hour (Maybe + 15 minutes) whether you take a cab or the underground. Unless I have baggage id always chose the train or underground (I live in E14)
Im surprised your delving into the rules and regulations for a £50 cab ride, when surely the cost is the least of your problems,
The bottom line is you cant fly from LCY with anyone now. Why are you fretting about £50?