well, when we started we had no preference, as we wanted any school that will support DC to attain his potential etc, so we were open minded really, why your preference for independent school? we did it the other way round, visited all state schools, then special schools and then independent school at teh very last minute ( all the others could not offer us a place, and did not want the private schools to cloud our judgement - very easily done). LA would want to see evidence - written evidence from all the state schools and special schools that says they cannot provide a place. they did so in our case. However if state and special schs cant offer DC a place, and independent can - then you are half way there. the psych report need identify the need to small class and why, note not all high functioning children need the small class, a few can be taught and supported in large class mainstream. However do note that you will likely go to tribunal to get this. Remember a Psych report is not specfically for independent placement, but gives more info into what support you DC should have in any school placement. and note some independent sch might say they can provide - could be money driven , so you need to do you research properly or else you will be fighting with them to get the provisions implemented properly- more hard work - as they follow their own processes unlike state schools etc. so its all about getting the right place.