In an investment bank, the trading floor is the first place to get any kind of activity. The early birds will turn up at 7 am, with more activity about 7:30 am. Morning meetings usually begin about 8 am. Yes there are a few people who are in the office before 7 am, but apart from people like security / catering / facilities management (none of whom will be flying to NYC) these people are comparatively rare
Allowing 45 mins from Broadgate (maybe 30 mins form Canary Wharf) to LCY (either DLR or taxi in rush hour) and 30 mins for checkin / security and maybe a little bit to spare, one would need to leave the office by about 8:20 am. - hence (as WHBM says), not really possible to do any substantive work in the office if one is catching the 09:40 flight out of LCY. All large firms in the City (banks, law firms, consultancies) provide 24h ability to login to their (virtual) PCs so someone who wakes up at 3 am and wants to do a bit of work can do this quite easily from anywhere with a laptop and Wifi