So, I bought mine from Metropolis Motorcycles at Vauxhall. Not sure I'd recommend them to buy the bike from as I had a few issues... However, they're right in central London and have a demonstrator. So why not take one out for an hour in London and see how you get on with it? You might find it's not as big as you think.
I have to get mine through a pretty narrow pedestrian gate to park it, and was really worried before I bought it that it wouldn't fit. I think because it's so tall and long it tricks the eye into thinking it'll be really wide too. But it turns out, no problems getting it through the gate.
So, I'd say give filtering a go on the demo (though be a bit careful! £1000 excess to pay if you damage it!) before you get too wedded to the idea of stripping the fairing off.