Hi, I have nc'ed for this as don't want to be outed.
My DS is at Mary and John and loves it there. I'm extremely happy with the school. I also have lots of friends whose children go to Larkrise (and one friend whose child is on the waiting list to go there). However, I suspect that neither school will have vacancies at the start of this school year (Mary and John is almost always oversubscribed, though I don't think the numbers on the waiting list are huge; Larkrise I don't know so much about). However, east Oxford is a mobile community like the rest of Oxford, in fact! and so the odds of a place opening up over time are high. There are lots of international families who move in and out of the UK, like you. So if there's a school you really want, you could send your DD to another school in the meantime, and then move her to your first choice school when a place opens up.
I also have close friends whose daughter goes to East Oxford Primary. Although that school's last Ofsted was disappointing, there is a dynamic headteacher and my friends are enthusiastic about the school. The proportion of Asian pupils is much higher at East Oxford Primary than at Larkrise or Mary and John, which means that some middle-class families in the catchment area tend to place their children elsewhere, but I think that's a shame.
Don't know anything about Windmill or Rose Hill, I'm afraid. The headteacher at Mary and John was formerly head at St Ebbe's, and my impression is that the school has gone downhill somewhat since her departure (as reflected in the school's last Ofsted report). The Christian faith is said to be promoted in a more rigid, less inclusive way at St Ebbe's than at Mary and John (OK, I'm showing my own personal prejudices here!). I've been told that Mary and John is the only C of E primary school in Oxford that doesn't use faith as a criterion for admission (so C of E applicants don't get bumped up on the waiting list, as they would do at other C of E primaries).
I'm surprised and disappointed to read about williamina's negative experience at Larkrise. I have heard only positive things about it. The state of the building does sound bad; you could ask the head whether that has been remedied. About the disorganisation: it's true that the quality of teaching in every school varies according to the individual teacher, so maybe williamina's DD had a particularly poor teacher. And poor communication with parents is something that the school's last Ofsted picked out as needing improvement, so I would assume that the school would be taking steps to remedy that now. As for no uniforms - I would LOVE no uniforms!
As far as Asian pupils are concerned, I would be very surprised if lots of Asian families from outside the catchment were sending their children to Larkrise. Children within catchment take priority, even over children outside catchment who already have siblings at the school, and the school doesn't have room to take in lots of children from out of catchment. So the ethnic composition of the school should match the ethnic composition of the neighbourhood pretty closely. And the neighbourhood is a mix of Asian, white British, Polish; of university academics and taxi drivers and so on. It's diverse, which is precisely what lots of parents - myself included! - love about East Oxford.
About there being a social divide at Larkrise between Asian kids and everyone else: Mary and John works hard to ensure that this DOESN'T happen, and I would be astonished if things were different at Larkrise. It's inevitable that kids will gravitate to some extent to the other kids they have most in common with (in terms of religion, upbringing, etc) but at Mary and John, school and pupils are proud of their ethnic and cultural diversity. My white British DS has plenty of Asian friends. The school has Asian teachers, teaching assistants and governors. Sadly, at school fairs and social events, and in the PTA, white British families do tend to dominate, so that the crowd you see milling around at a school fair is not going to be as diverse as the crowd of parents you see at school pick up time. But again, the school is aware of this and tries to ensure that all members of the school community are recognised, valued and included. A few examples of this include: some Asian families are reluctant to let their children go on the annual year 6 school trip, which involves 5 nights away (I think?). So teachers talk to the parents involved individually to see what their concerns are (sometimes they even visit them at home) and to reassure them that the children will be well-supervised on the trip, that Muslim norms about modesty will be respected, etc, and every year all or virtually all the yr 6 pupils end up attending. Also, our summer fair happened early this year so as not to clash with Ramadan. When a boy from Egypt joined DS's class one year speaking only Arabic, DS came home after a few terms and announced, 'Mum, I'm so proud of Mohammed! Our whole class is proud of him because he came here not speaking English at all, and now his maths are already so good that he has won an award!' DS was very young and the time and was clearly parroting what the children had been told in school assembly, but I was happy to see the school recognising a new classmate's efforts in this way.
All this is of course about Mary and John, not Larkrise, but from the sample of Larkrise parents I've met (and some teaching assistants too), I would expect the approach at Larkrise to be much the same. With all due respect to williamina, 2 months is a very short time to have your child in a school. She would have been barely settled in by then! And if you go private, you opt for an environment that is incredibly un-diverse. Humph. What my DS is getting from state school is something that money can't buy, namely, the chance to work and play with children whose backgrounds are utterly different to his own. And to learn from them.
OK, I will climb off my high horse now.
Good luck, lucy, and welcome!