You're not over-reacting, the threat is there but it's how you chose to deal with that.
We, as parents, worry for a reason and if you don't feel comfortable don't go because you'll pass on that worry to you child.
My son goes into London all the time and I worry like crazy but at 20 he can do as he likes, however he promises not to use the underground. I don't think anyone can talk you out of being worried, I think your gut reaction is to want to protect your child.
Do what you feel is right for you.