Is having your hands "on the hoods" of drop handlebars safe for braking? I've never had a bike with drop handlebars, but may get one for commuting in busy London (likely a single-speed with mechanical disc brakes).
This would mean riding with my hands mostly on the hoods, but it seems like a slightly awkward position to use the brakes from:

Riding on the drops seems to offer better access to the brakes, but is apparently &quot;less stable due to narrower hand position&quot; anyway — so when talking about cycling with cars, vans and busses around, doesn't seem like the best choice either (for a non-professional).

Overall, is that just all in my head, or is there some cause for concern?

Also, is there any reaction speed data compared with flat handlebars, or other such studies, for this?

Personally, I'd be most worried about situations where I need to react quickly, as well as situations that are usual but I need to be consistent in my braking.
Flat handlebars are like second nature to me, would those be safer?
I commute every day in SF with drop bars. It's not an issue for me. You quickly adapt to the hand position, if you bike is set up in a way that is comfortable for you.

The real safety issue you should be worried about, IMHO is not braking itself, but rather the "heads-down" position you can be in on the bike itself. You have to get used to looking around you/behind you for cars, etc. That's why your position/comfort on the bike is so important. 

You can also install cross/interrupter levers for a second braking position option, usually at a nominal cost (not sure if this works with your particular breaking system).