Whew, so many replies! I'm really glad that there's such a variety of views and experiences (rather than just outright condemnation ), and thanks to everyone for all your points.
To answer a few points...
Why don't I take her into the supermarket with me, but usually leave her in the car? Mainly because she whinges and asks for stuff the whole way round if she comes in - we have a particular 'issue' at the moment about her obsession with shops and buying things for the sake of it. I know that if I leave her in the car she will have her nose absolutely buried in a book. She's happier, I'm happier. Obviously I wouldn't do that if it were too hot in the car, and in fact the reason for leaving her at home on two of the occasions was that it was really hot and she wouldn't have been comfortable in the car. I acknowledge that there are small risks in her sitting in the car, but a supermarket car park seems a very unlikely place for the abduction of a very loud and confident child. I'm a fast shopper and would never let 'an hour stretch into two'. If she's in the car then I'd be a maximum of half an hour, if at home then probably more like 45 - 50 mins.
Regarding the boundaries issue... she doesn't get away with much at all! I'm very firm with her on lots of things (have to be ) and she gets told 'no' on a very regular basis - there are legions of things she has to do that she doesn't want to! I know that she doesn't feel scared to be left, as some of you were, in fact, she's always pushing to be left at home when we go out to walk the dog (the answer's always no), and to be allowed to go out on her own "on an adventure" or "to run away, but only for half an hour" (the answer's always no, although we did let her go to the local shop once, with DH following a bit behind her ).
She wouldn't make toast, so no knife in the toaster. I lock the front door with a key, so she couldn't open it, and she knows to ignore the door if there's a knock. As I said before, the layout of the house is such that she can exit into the garden from the living room and stairs. Her falling down the stairs is a good point, actually. Coll2010; you make some very good points, and this is why I felt uneasy about doing it.
I've left her at home on three occasions. The first time was actually just to nip to a shop just up the road - I was gone for twenty minutes. I didn't have any concerns about leaving her as she was engrossed in a book and I knew she'd remain so. I still drilled her with all the safety stuff though. The other two times have been for me to go to the supermarket a mile away, and I chose to do so because it was so hot. Normally, if I take her with me to the supermarket (rather than going while she's at school), it's because we go to the library for her to get new books (parking in the supermarket car park), then I leave her in the car reading them while I do the shopping. I park near the store entrance, and tbh, if there was a problem, she would come into the shop and go to the service desk. I don't feel unreasonale doing this, but maybe I've done an aibu by stealth here .... aibu to leave my 7.5 yr old in the car with her nose stuck in a book while I go into the supermarket (weather permitting)??
Thanks Seeker, Cory and Piscesmoon for emphasising that it's not all cut and dried, and that whilst there's always the chance of something awful happening, we can't let our lives be ruled by the fear of it.
On balance, it's certainly not something I would want to make a habit of doing, and would probably only do it again if my neighbour were in and aware that DD were on her own (she'd hear any falls, thumps or screams). The supermarket car park is another matter though...