Isn't it all done on exam results? State schools don't interview or look at SN at this stage, in my experience, unless you are asking for extra time. And there are so many clever clogs applying that you need pretty good marks in all three papers.
Hi Wotnow, just wanted to add that I was a Latymer student in the '90s, and they weren't that hot on SEN then - the ethos was very much about about independent learning, without much in the way of pastoral support. Having said that, I know staff who now work there and they do seem to have quite a few children with (mild) Asperger's nowadays, so it could be that their awareness of SEN has improved since my time. They've always been hot on maths and science, so it could be that your ds's talents stand him in good stead, but be aware than there is a verbal reasoning element to the test too.