Where do I start?

traffic is not that bad at 7:30 in the morning... and i get to speed down finchely road (downhill all the way) before going through Hyde park...(so much better than the tube...)..only have to slow down when i get to high street Kensington...

fixed wheel is more likely to slow your commute down, if anything, as you'll have to learn to spin damn fast where you would otherwise be coasting.

what's wrong with someone overtaking you? the girl on the fixed may only have to go 2 miles, maybe she was putting on a burst of speed, there's a good chance she'll still be overtaking you whatever you ride.

if you want to be the fastest rider on the road then:
a: don't get a fixed wheel and,
b: prepare to be disappointed.

in heavy traffic and complicated routes with lots of junctions, a fixed wheel bike (in the right hands) can be an excellent tool.

not so for blasting down a hill.

I'm not trying to be a cunt here, just pointing out a few things for your information.

a langster for £200, IS a decent choice.