Whistling British wind aside, the Regent Palace Hotel is your best bet for single/double rooms in Piccadilly Circus. At (per person rates I had in spring 2006) $40 vs $32 at the service-less nearby Piccadilly Backpacker's Hostel, the Regent Palace wins in a no-contest. Piccadilly Circus lodging is spendy, though, and you *can* get a dorm bunk at the Piccadilly Backpacker's Hostel for around $20 / night, though there are far better hostels to be had in London.
