No, I'm pretty sure we have a fair understanding of that, as we do with most things that go on on our own soil
It's not a terrorist attack, it's one of many foiled attempts. It just happens to be that this time it was directed at both the UK and the US and purpotrated (as with the 7/7 tube bombings) by British citizens - it was equally an attempt at an attack on us too.
Really, there's nothing to worry about any more than there usually is, and if people are worried about it usually or from day to day, then the terrorists have already won without 'winning' that many battles really.
Seriously. That's why we have security procedures and services. They are just as trustworthy in these matters as your own really.
It doesn't really mater who was on the planes. People are still people, and the thousands delayed at airports were still confident enough to get on the planes that could fly today, so why should you or I worry about it? Besides, why should the date matter. 9/11 was the date of an atrocity. Whether something happens on an aniversary of that or not really makes no difference unless you want to make it significant in your own mind. It's only a date after all - it's the memory of event itself that matters, and even there it's an event in the past. Granted, it was a terrible one, but it's nothing to be scared of now. All we need to know was that it happened, it was awful, and that we've hopefully learned enough lessons to prevent it happening again.
Given that you are so greatful that no Americans were hurt, I should imagine a little faith and maybe even a thankyou to the London Metropolitan Police and MI5 are in order.
(that's more than they's get from me! I pay their wages!! lol ). There's nothing to be scared of when it all goes right. It's when it goes wrong that there's a time to worry - if such a time exists even then.
Seriously - this is wisdom that the UK has learned the hard way through years of attacks from both outside and in - Don't let the buggers get you down and they won't beat you down
(even if the UK media insist on ignoring it in a vain and scare-mongering attempt to sell themselves to us. lol)