Having breakfast in the City of London, or indeed any financial centre, is less common than it ought to be. I don't like having lunch for lots of reasons, not least of which is that it takes too much time in the middle of the day, disrupting work, and requires me usually to eat more than I should, or at least tempt me to do so. I am trying successfully to lose weight, not gain it.
Persuading people working in the City to meet for breakfast is quite hard, as that is the part of the day when most is going on. And even when they do, I haven't found many exciting places to take them that also offer some element of discretion and opportunity for private conversation.