Oh Doin, it's exhausting, isn't it. My DS used to try this kind of blackmailing a lot.
She's playing games. Don't play with her! She'll be in trouble at school if she doesn't go, which she will know, and I don't think she'll want to miss a non-uniform day because they are generally popular and fun.
Don't rise to it. Say to her (as calmly as possible) "It's up to you. If you don't go, I'll 'phone school and tell them you're playing games, and you'll lose privileges at home. Night." And go to bed!
When you go to work tomorrow, if she doesn't go to school, then call them and tell them why she's not there. Take the router/laptop/whatever with you if you need to. But it might be easier to simply block internet access (if you're on BT broadband I can tell you exactly how!). Or if you are comfortable switching your power off at the mains (just flicking the big switch in the mains box) and you know she won't know what to do about that, that is far and away the easiest thing to do!
Don't even talk to her about it when you get home.
Leave her to sort out any trouble at school. She will at least get a detention. My DS's school used to put them in isolation for a day for truanting.
I have mixed feelings about 'making it miserable'. It depends on whether you can do this without engaging with her at all. You basically need to give her NO response to this kind of blackmailing - and I'm afraid that 'making it miserable' probably counts as a response. She wants your attention and your reaction, and if you get upset or cross, if you nag or shout or lecture, then she has got it, and she 'wins' at the game she is playing!
But you certainly need to make it very very boring!
Oh and don't worry about a day of school work. A day is only a day. And it's much less important than dealing with this situation effectively. :)