I’ve NC but if you search under my username you’ll find an old post where I responded to a question about Surrey preps recently with some background (some personal experience, some more general local feedback).
I’m surprised you moved here without a school as it’s well known for being competitive, can I ask where she is at school at the moment and what you think her strengths are?
It depends on what you’re looking for as to what the right choice is re London / here. As you’ve probably found, the most popular schools are all at capacity and waitlisting for places in her year. Schools will mostly know their availability for Y2 now as existing parents are on a terms’ notice for fees. I would expect you’ve found Feltonfleet and Milbourne at capacity. Maybe also Surbiton? I would expect there would be availability at Daneshill as it’s enormous and they move up to the prep in Y2 (they also add another form of 20). I would expect you’d also find availability at Claremont, Notre Dame, possibly at Rowan. Downsend move up to the “big” school in Y2 I think so again there might be a possibility there.
However, the good thing is that many schools do have a big new intake in Y3 and the closing date for entrance exams (usually taken Nov-Dec) has not yet passed, in addition to those above these include LEH, Rowan, Feltonfleet, Guildford High and Surbiton High (I think?).
So there are two options:
Plan A
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Find a school with space in Y2 that you like and want to keep her at until 11, you really have to see places to make your own decision. Post back here if you’re struggling with a decision and you might get some more help, my other post has some more info
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Find a school for Y3 onwards and register for the exams PDQ. Then just get her in somewhere (or keep her where she is??) for Y2 and either make sure it’s good enough for you to be confident that she’ll be ok with entrance assessments (depending on type of school.. remember they do value personal skills, not just academic), or else supplement her learning with some extra help like Kumon now (considering Y3 assessments are in 6m time). In this situation, a London school if it’s good might not be a terrible option as it would only be for a year and she would be well prepared. I would only consider this if you were driving her everyday though, I think it would put a lot of pressure on her... also how much are they really going to teach her in half a term?
Other options that are easily accessible but I don’t know much about are Manor House and Ripley Court.
Many children do travel some distance to preps even here, so school buses are frequently used and are good to think about.
Good luck