ETA my husband's comment, which is actually a much better point than the one I made below:
They're Loyalist protesters this time. Why on Earth would they start bombing London? They might knock over a union flag!
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Let's say that you're not overreacting-- which I'm not conceding, but let's just pretend. What are you going to do about it? Honestly?
I understand it must have been really hard to deal with 9/11 (I was halfway across the country, and I still don't like to talk or think about it), and no doubt your dad has some stories.
But, my own personal take on it is, there's nothing that I can do anyhow, so I'm not going to worry about it. There's not a single precaution you could take in your everyday life that would: a) not leave you living like a prisoner in your own home, or b) actually make a blind bit of difference in the case of an attack.
So my advice is generally to relax. By all means, if you find yourself confronted with an Orange parade or something, turn around and walk the other way. If you see a bunch of men in ski masks loitering and looking shifty, consider phoning the police from far, far away. But other than that, just live your life. Don't lose sleep over it. It won't help.