For your budget, and since you'll be coming in a few weeks, I'd wait, especially if you are coming to London. In that price range, I can't imagine flats staying around long, so maybe think about doing a short term house share to get your bearings first while you look for places. This might help with getting you a landlord reference as well for when you find a flat of your own.
But yes, it is possible to get yourself a flat within a week, especially if you have easy access to funds locally.