I'd counsel that there's no 'ideal' London commuter. What's best can vary enormously depending on your route - distance and from where to where...
e.g. London is largely flat so if you work central but live Zone 3 or closer then singlespeed road bike (c 70 inch gear) will probably see you right. But if you live the wrong side of the Crystal Palace ridge then gears may be better...
Equally if you're carrying a lot of stuff then panniers become necessary and therefore gears a better choice.
But gears can be a right pain with all the stop/start of many London commutes - traffic lights/junctions/traffic jams etc - constant changing down and then up again. I find a singlespeed ride much less hassle in this respect.
My favourite commuters have been:
A singlespeed Roadrat with flat bars and disc brakes - very nippy, upright position and stopped very well. But the rear axle couldn't take the force of the discs and the rear wheel slipped all the time, and the horizontal dropouts made full mudguards a hassle.
My current Condor Tempo is my favourite - singlespeed steel frame with dropped bars and decent quality dual pivot brakes. 25mm tyres and a carbon fork + full mudguards. A London bike for London riding. Not cheap but you get to build it up exactly how you want so you don't ever need to upgrade anything.
2 main things I would think about:
1. if you;re leaving it locked up public on a regular basis then either get something you're not too worried about getting nicked, or that can be heavily disguised
2. Get your Bikeability training free from your local authority - anticipation + proper control of your bike win above disc brakes any day in my book
Despite the stories you hear, I find London riding more enjoyable than out of town - it's a great way to see a beautiful city, often the quickest way to get around, drivers are very used to cyclists these days and there's a real feel of London being a proper cycling city - just from the sheer numbers around