So here's a question: Are a lot of those that are anti-uniform in that mindset because of the poor way they were handled with it at school? It seems that many folk who are anti it have a bit of an issue with the way they were treated, and on the contrary many who are for it found uniform helpful or them in the past.
I am anti uniform for primary and secondary, but especially primary. May be an age/generational thing. I went to a rural school - which now would be OFSTED 'outstanding' by default as only richer people can afford to live in such villages, but in those days it had two huge council estates and a very mixed demographic. The Victorian school was very old fashioned with some real old battle-axes for teachers, and strict discipline - but of course, as was usual then, no uniform whatsoever. I don't recall a dress code (apart from navy blue pants for PE!) but there may have been one. Oh the shame, my mum once bought me royal blue knickers - that was a trauma in itself!
At what is now Y3, the boys went to a separate Boys' School which did have a uniform; the girls continued at the old school, without. So my brother wore uniform and at the same age - I didn't.
Later the old primary schools were replaced with a modern, open plan, lovely new one where I did my last 2 years of primary. The contrast was stark - from the strict old Girls' School (no uniform) to the hippy open plan 70s' progressive school (no uniform). Very different schools with radically different approaches to education - the lack of uniform had no impact on our ability to learn in either a strict, old fashioned, academic kinda school and the modern hippy sort.
High school had a uniform. I was one of the poor kids so maybe that informed my hatred of it. It was no leveller. I wore the same (home-made) skirt for 5 years. Bri nylon shirts. They did allow you to wear any jumper so long as it was the right shade of blue so many of us had handknitted ones (much more practical and warm) although my mother was dead, so I didn't. I was bullied at school but that was nothing to do with my crap uniform. In fact when kids twigged that I had holes in my clothes, darned tights, etc etc etc - they were actually kinder to me. I'd have no reason to loathe uniform based on that experience. I just would like to offer a reality check - it is not, never was, never can be a leveller. It is the opposite.
Later as a teacher, as I trained, the Thatcher/Baker tory 'reforms' were coming in so perfectly sane non uniform schools were just switching over to uniforms. It was mad. The kids were well aware who was poor - just as we had been. They were well aware who was neglected at home; who had B.O, or greasy hair, or a 24 stone mum. Kids are cruel - they are also hyper alert to 'otherness'. They spot your mum looks weird when she comes to pick you up at home-time... they will remember that three years later at high school when she no longer picks you up. They are all perfectly well aware that so and so's dad is a rich builder; someone else's dad is on the dole...
I have taught in a posh school in the US (no uniform or dress code). That was great. I have taught in rough inner city British schools where the kids were poor as poor can be but the parents were still expected to shell out for uniform.
I have done causes on Parents in Education as part of a Masters in Education and uniforms is an interesting subject as they are often very popular with parents for all the reasons people cite above. But the reality in the classroom is, they do nothing to facilitate anyone's education. Ever.
They do however, please right wing governments and politicians who believe that making everyone 'the same' somehow may make them better, more compliant, future employees. Ironically it's quite a Soviet concept, when you deconstruct it.