Hi MrsOakenshield:
Our DDs go to a highly multi-cultural school that is a veritable United Nations.
Things we parents all have in common: we all want a good education for our children & we all want the best for them (including a nice circle of friends).
I suppose the question to ask yourself is why are you judging the school on its mixed ethnicity? Why do you think children from other backgrounds don't desire to have play dates or seek to arrange them?
My DD's best friends are Filipino, Chinese, Indian, Afro-Caribbean, Korean, Sri Lankan and Syrian. The families are amazing - some are here because of harrowing circumstances in their home countries and are incredibly grateful for the normalcy British life offers them and their children. All are very aware of international education standards and bring that pressure onto the school (indeed it is largely the 'foreign parents' who politely or otherwise encourage the school to raise standards, improve communication with parents, etc...).
Not being prejudiced - but just picking up on a trend I've been quietly observing in the playground these last 7 years - white British boys are quite often the problem. (articles/ research backing this view on FSM white british boys here: news.bbc.co.uk/1/hi/education/8485016.stm and Joseph Rowntree Association research here: www.jrf.org.uk/media-centre/white-british-boys-most-persistent-low-educational-achievers-practical-measures-could-i).
I can't speak about having a son, but as someone with 2 DDs (and I see you're talking about your DD) I've personally found a wide circle of friends from a variety of backgrounds to be an incredible experience. It's a real honour being invited to their home for a play date or a meal, to be invited to a traditional Indian dance gala, to come along to Chinese Saturday school or Korean Saturday school, to attend festivals with friends and equally those kids enjoy more typically British things with our kids, like picnic & playing in the park, days out to theme parks, block party for Royal Wedding, days out to castles/ historic houses, etc...
My advice is start each day off at school saying hello. Make a point of introducing yourselves to parents and learning your DDs friends names (I do forewarn you that in Year R this can take months - both DDs were terrible about remembering names at first). Throw a birthday party for your DD and invite as many as you can. Make the first move - and invite a good friend over during the first half-term or Christmas break. If you do not behave as if being friends with them is a problem, you'll most likely find they won't mind either. Friendships with children take a while to form (maybe 1 or more school years - we certainly found Year R children played alongside each other and Y1 friendship groups solidified) - but friendships between parents take years, shared experiences (good or bad) and some work.
Please do not expect Day 1 or even Day 60 - to have your DD settled into a large group of friends and having all sorts of play dates.
One piece of advice I was given, which did help break the ice, was to have our DDs join after school clubs, take dance, take up an instrument, join a choir, join rainbows, etc... thus having friends both within and outside the school. [a useful buffer when friends at school are a bit off with you - which does happen I'm afraid]. Over the years it has meant that pretty much anytime we're out and about (and we're in a huge city) we always run into someone one of the girls knows.
Finally - please remember starting school really is harder on the parents than the child. Primary school is a lovely time, but isn't always smooth sailing. If it goes well - fantastic. But if it isn't going so well, try to remember it is only 7 years of your DDs whole life - which if the papers are correct is likely to stretch to 90-100 years. If primary wasn't great, senior school may be better.
HTH