Thank you all! Gransnet is such a help in situations like this. I knew all along my instincts were right (right enough anyhow!) and all these comments confirm that. Between you, you have covered all the points that were trooping through my head, things like the possibility of an alcoholic midnight feast scenario which I don't think Minibags would be comfortable at, the legal aspect, and more.
Like several of you, I've no problem with teenagers having an occasional alcoholic drink in a situation such as a dinner or a party where adults are present and where the purpose is not to get pissed but simply to enjoy an alcoholic drink in a non-riotous social setting. Thinking back, I think Minibags did accept a small taste of champagne when we were celebrating her sister's university degree graduation. She didn't like it enough to drink all of the quarter glass we gave her to try, so I cannot imagine her feeling comfortable with a bunch of girls who, according to her, have all been imbibing alcoholic drinks since they were twelve.
Several of you mentioned peer pressure. I felt I was being subjected to parental peer pressure too. It might have felt different if I'd known the parents but I don't. Then there is the peer pressure on her if she went. Just imagining what that could be like makes me shudder – it's hard enough to stand up to it when you're a mature adult and know your own mind, never mind when you're just fifteen.
In the end, I told M to tell her pal that if I sent a text it would say that I didn't want her to have alcoholic drinks (I also told her I wanted a promise from her that she would be sensible). She was OK with that. Message came back, via the birthday girl (at no point has birthday girl's parent contacted me directly, which is another thing that makes me feel uneasy: it's all a bit too casual for comfort), that the others wouldn't be allowed alcohol if M wasn't. Since the apparent purpose of the party/sleepover is an experiment in getting drunk, I don't think M's presence at the event would be all that welcome!!
So now I'm hoping and praying (atheistically of course!) that it is in fact a bit of a relief to M that she has to turn down the invitation. It's certainly a relief to me. Sad because I'd have had no problem with a "girls being silly" sleepover. Too many people seem to think you can't have fun without being drugged one way or another