All may not be lost!
After what seemed like about five hundred attempts (but in realiy can't have been more than two or three hundred), I eventually managed on Monday afternoon to complete the secure 'failover' form and get a page thanking me for my order.
So I sat there like the smug little git that I am, feeling very pleased with myself that I had just managed to scrape in before the phones were sold out, until I read on this thread that quite a few people had got the same message as me, but that their orders hadn't actually gone through. At which point my smile slipped somewhat, and I checked the order status on my O2 page, to find that, sure enough, there were no orders listed there.
So I resigned myself to having to wait until new stock arrives in the UK, because I can't get to an O2 store for 8 am on Friday, and I expect that they will be sold out by lunchtime. But a few minutes ago, an email arrived from O2, thanking me for my order, and giving me a tracking number. And it has appeared on my page on the O2 site, as well. Now, it doesn't tell me that it will be delivered on Friday, but it doesn't say that it's backordered, either, so I'm hoping that it will arrive on Friday. So if you got the "thank you for your order" message, but no email, don't give up hope: it may be that they just haven't cleared the backlog as far as your order yet.