I'm gonna go slightly different from the others here and say I'm not so sure I would have placed my kids in the multi-cultural alternative.
If for example I was still living in an area in which there was a heavily Moroccan dominated school I could send my kid to, and a more white alternative that has some racism, I'm not sure I would have been able to stomach sending my kid to the Moroccan alternative, because of the other traits and influences they would pick up. This isn't just islam I am talking about, it is ghettofied Moroccan cultural mentality that I would kill to avoid placing my kids in to.
Bearing in mind I'm a single mum, even more so, since kids in all schools will find a way to bully the kid who doesn't fit in with the appropriate background.
I honestly don't want my kids to pick up the mentality that they will if they attended the same school my sister's kids do, and judging from her kids, I'm pretty pleased I've avoided it.
Also, on the racism front, my kids do happen to go to a very mixed school locally to me, children of all flavours go there, and yet my own son, who is a mildly olive skinned, and practically white in the winter......is still called a paki.
My daughter who is taller than other girls is called fat, my eldest son who goes to a boarding school is also called paki, but he is much much darker, like me, and thus you can understand the geographical mistakes the racists make, less so with my practically white son.
Kids are uneducated assholes in any school.
Yet, my kids are doing well and find it humorous thanks to my support and home education, and of course my continued contact with the schools to remind them to educate the children they are teaching.
Of course problems may yet arise, but for the most part my children seem happy, and I am still so relieved at how different they are mentally, to my sister's very Moroccan-muslim children, who bear all the hallmarks of a rising experience of teenage hood on a level I experienced it.... horribly.
Still though, I do have the option of very mixed schools, and not over populated by any race, and so I am not in (excuse me, I have to say this) such a black and white situation.
I also moved from Yorkshire for the same reason you are experiencing now, because people would walk past me and my son and call us Pakis. I found in the long run it was too much for me to take, so I do understand where you are coming from.
I just wanted to point out that even in a multi racial school my kids are still called names, it is stupidly unavoidable with pig ignorant parents roaming around out there.