It would help if you said how long the connection time was!
LCY is a small airport and so arrival and then re-clearing security is very quick. Remember that for people starting at LCY check-in closes something like 20 mins before the departure - and that's if you have luggage - and 15 without.
You would only be off loaded if your flight from DUB was very late. They won't hold the BA1 for you. If that did happen then the BA3 would also be an option.