Invisible Umbilical Cord

I grew up in a small Scottish village of 300 houses.  When I was wee, my mum didn't seem to have any issues with me walking alone through the village, going to the shops, or visiting my friends.  In fact, more often than not, I'd be sent outside (alone, or with my similarly aged nephew) and lose myself in the woods or the beach.

I'm a mother of two children; my 15 year old son, and my 8 year old daughter.  Our daughter was born just after we moved into Nottingham, and yet, I still don't feel safe letting her walk to her friend's house, which is only about 8 houses away.  Is this a product of news distribution? Do I worry because I know that children get kidnapped?  I love our neighborhood and haven't heard of anything untoward, and my son has been roaming Nottingham/Perry Hall for a few years now.  Is it because it's my girl?  Does her gender alone put her into a demographic that I can't help but feel are intrinsically more likely to be targeted by unknown scary people? 

Let me be clear, I don't fear my neighbors; we're culturally diverse spanning the globe, most of us have children, most of us work.  We're an ideal subset/cross-slice of American blending.  Are we so ingrained by the fear that someone could sneak into our neighborhoods and steal our children that we hold them too close and not allow them to experience a day lost in play?

I know that as our daughter gets older, she'll spread her wings more and we'll trust that she can take care of herself, but for right now, she wants to be independent, but we're not quite ready to throw her to the fates.

What kind of experiences do you have in letting that invisible umbilical cord stretch just a little more?