Alana Last year on this thread there was someone coming back from an International school in the same posting as we returned from ten years ago now. She was panicking because she had encountered the uber competitive mothers at the St Paul's exam and her daughter had had no tutoring at all. She is in Year 7 there now. I had the same experience. In fact I have done the entrance process from both relaxed International School and South West London Prep and I far preferred the former, more relaxed and much easier to maintain a healthy perspective. I did do some DIY work with my DD but just to cover the parts of the curriculum she hadn't yet covered, and exam technique, but nothing on the silly scale it happens here. In both cases my untutored girls got into all four schools they applied for, ones most frequently discussed here.
The playground at a South West London Prep in November / December / January is a scary place, and I developed the skills of a SAS hostage rescuer so quickly did I get my DD out of the miasma of competitive / panicked anxiety and away from the Chinese whispers about what was required, which bore little resemblance to what the schools actually require. What you realise after, and especially when you encounter all those bright girls from state schools and overseas backgrounds, is that the children get to the school that they are meant to be at given their ability and personalities and all the tutoring makes minimal difference because the schools don't want heavily tutored pupils who will struggle when they get there, and they are quite good at spotting ability. And yes they take an overseas background into account, as one Head told me when we came back for the interview. "They get so much out of it and have so much to offer our community as a result of all their experiences."
At all these schools you will find plenty of other pupils from overseas backgrounds. When my DD started I asked if there were any other expats starting and the registrar who was normally lovely sniffily said " Yes but she has returned from ... (European country) so they won't have anything in common" She is still her best friend.
Also do not get caught up in the crazy South West London judgements on the schools according to some silly notional academic league table. Schools like LEH do better because they are more selective but these are all good schools and enable bright pupils to get strings of A*s and to Oxbridge (even Ibstock though I have some serious issues with that Head who seems responsible for more refugees from that school, especially amongst expats attracted by it's old reputation of being more akin to a relaxed International School, and those with mild learning difficulties that schools like LEH are happy to support, than any other I know of apart from Hampton Court House, casualties of her relentless drive to rise up those league tables). Choose the school that feels right for your DD and don't be swayed by academic results and green acres (I speak from having made that mistake, in spite of dreaming the night the decision was due that the school that she ended up in sixth form at was set in elysian fields with sixth formers welcoming her in like angels 
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Amidai and others. I have a background in using VR and NVR in recruitment and employers and a lot of the indies, and it sounds as if that is KGS included, invest money in making sure the tests are unpredictable and therefore untutorable. It makes them much better indicators of ability. The problem with the Grammar School VR is that they appear to have failed to keep developing the tests so that with practise you can improve your scores, hence the scandalous tutoring industry (much debated on other threads). It may be that KGS have made the test more challenging as well as unpredictable to better differentiate those with higher ability. I wouldn't worry too much as it suggests to me a test that will have differentiated those with the greatest ability as opposed to those who have sat in tutoring factories.