When my August DD1 was in year 5, she finally complained that the maths set was too easy, and her friends in the upper set were doing fun stuff like sweet shop maths. I went in with her to see the newly qualified teacher, who was clearly stressed but open to ideas, and she suggested that DD try the higher set, and could go back down if she found it too hard. She never moved back down. I feel this meeting also drew attention to my quiet DD that was needed.
At the parent meeting later that year, the teacher said that DD's classroom output was better than the test results, and perhaps she "didn't test well". Meanwhile I was tutoring her esp in times tables (her good memory meant this was useful for her) and weak spots like telling time and exam technique, which helped. Her confidence seems to be the most important aspect.
Ed psych reports seemed too expensive but maybe it would have been worth it. I'm still considering it for my own interest.
I am really glad to hear that worked for you. Unfortunately, some teachers are far more obdurate than that, even newly qualified. Hopefully Studio1972 will not have to go to the expense of an Ed Psych report, and if he / she does, may still find that the school comes up with some justification to ignore it rather than give the child a chance in an upper set. However, I think if you are firm enough and leave a clear enough paper trail if the school is, well, "sticky" shall we say, there are few that will completely ignore you as they worry that OFSTED will see the paper trail. The thing is you have to move fast. Year 6 is soon gone. Children can make a lot or very little progress in the next two terms ( and I would suggest this is generally not down to "developmental spurts" in a case like you have described to us Studio1972 - but to what the child has been taught and practised that is relevant to the KS2 tests).
The benefit of a private Ed Psych report is that you should be able to get one done within the next week if you get your skates on, and then, if it is clear that your child falls into the top x% that one might expect the top or middle sets to be in, you will feel more confident in stating your case as you know it is not just you imagining that your DD is more able than the school has been telling you she is for the last 3 years at least.
Hopefully you will be able to discuss your concerns in a really nice two-way discussion with the school, and they will take action. But if it is a bit tougher than that, you will have to consider if there is a downside to being a bit more assertive about the situation. I have been through some extremely uncomfortable situations. They have not backfired on my children. Sometimes when I say to myself, why did I bother, it might just have worked out eventually in the end, I imagine explaining to my child 20 years from now that I always knew they were in the wrong set at school and being taught nothing, but it was too uncomfortable for me to do anything about it. That stops my doubts.
Of course, you do need to be sure. You don't want your child struggling with work every day that they really cannot do. That would be worse for their confidence than wrongly being in the bottom group.