Weird. I booked a cheap last-minute flight to the UK on the internet at the last minute a few years ago, didn't have any trouble getting past immigration. I kinda figured I was going to, too, since I was coming from the US, and was an Australian citizen. Basically just got asked how long I was staying - "Two weeks", trying not to think about Total Recall - where I was staying - A Marriott hotel I'd booked for the first two days of my stay - and that was it. Must just have got immigration on a good day.