As a regular weekly commuter from LCY, and to maximise sleep in the morning before a 7am to Edinburgh, I would aim to arrive around 6.30, but I know city airport very well (although it's not that big) and can almost count steps from taxi rank to the security gates through to departure hall! 40 mins should be the most you need and as other users have said, 30 mins will give you more than enough time! If you think you are running late with security, let someone know and they will let you through to the tensa barriers quicker! Enjoy CE from LCY!