Huge City, not easy to navigate. London is expensive and not many bikes or bike shops snuggled together. You'll spend a lot of time on the Tube. I had better luck basing out of Oxford. Lots more bike shops nearby.
But getting on line and shopping before you go is the best way to go. Find a trustworthy shop and try to make a deal before you arrive. Have them set the bike up to your spec, fly in and ride away.
I spent about $700 hanging in London and traveling all over UK looking for a bike. Would have been better off just trusting a dealer, making a deposit on line, show up, load the bike and go. London is expensive. If you have friends to hang out with, good. But I would find the bike before you get there.
Great choice of bike, BTW. The Brits have no clue just how good the Vstrom is. Best value in the world today for long range traveler.