13+ mum here .... excellent advice above, so hopefully the following might help. We are in the independent sector and still get confused, so be assured you are not the only one.
Lingo:
Pre-prep is usually referred to infant school. Up to year Y2. A Pre-prep to prep school covers infant and junior
Prep school - Form 1 to Form 4 usually, which are Y3 to Y6, with some of them going up to Lower and Upper 6 which are Y7 and Y8 each.
ISEB is (from what we are understanding) a system/test that was hugely used this year as a sieving type of method. As the child does the test, the test in the computer starts getting harder or remains within the initial level as it started, depending on the child's ability. The results allows the schools to chose their candidates in a more straight forward way for them.
CATS results for the schools you mentioned, are, I believe, around 132 minimal. Prep schools have a good number of children with these and higher results. For example, in our DC's class, a good number scored 135 to 141 (I will relate this a bit further).
"The Process":
The system just changed a few years ago and I think this is why we are still a bit confused. This is also the reason why you apply at this stage of 11+, even if you are going for a 13+ placement in 2 years' time as we did. But there is hope! Some schools, such as Kingston Grammar has a small number of spaces reserved for 13+ (I believe they have 10). There is always movement and you might find a placement in a less selective school, in Y7, 8 or an offer for Y9.
So, the potential schools either used ISEB, followed by an interview and in some cases a math and English exam within it. Some did the ISEB, interview and soon the students will be seating their entrance exams, a favourite one following this pattern is Winchester, they are going to seat their exams in May, I believe.
Other schools had their own entrance exams, followed by an interview and then a placement offer or a conditional placement offer in view of your child having to seat common entrance exams (again!) in Y8. We applied to 2 schools, one gave us an unconditional offer, the other a conditional, all depends on the school.
After the exams and interviews, then the process either follows more exams, or an offer, waiting list or a decline letter, but you should always hear back from the schools you applied.
In the middle of all these, if your child did well in the exams, they ask for your child's current school to send or they look at the already sent reference letter, this has a lot of weight in them offering you a placement or not, but but but if you child didn't do well in the exams and/or interview, no Head can get your child in by reference alone. This is where the CATS play a role! In that reference letter, the schools send the CATS (if they did them) results as well as part of this letter. With results over 130, they will emphasis these as they will show any school an added potential on top of their results.
13+ entrance. During our 2 years, the school we chose (as it was a conditional placement), will then be asking for a further reference each year to assure that the child is in the same school they applied with, and continues with good progress. Again, this letter will not get your child in the school, but it can get your child out of the school before they even begun! If the 13+ school offers an unconditional placement, then that was it, a reference letter each year and all done and dusted. So no Head can get your child in a school by recommendation alone, unless they are friends or relatives among themselves, which is possible, otherwise the mere commoners like us, have to follow the process.
In the 13+ exams you will do the core subjects, English, Maths and Science plus 2 or 3 other options, most common options will be a language and a humanity subject. The minimal pass is 55% for them to continue or offer you a placement.
Your ("possible") options:
You mentioned that your child was not given any offers, but you don't mention if he is in a waiting list or it was a rejection letter. If it was a rejection letter, before you waste your time and money, call each school and find out if they will give him another chance in Y8 to seat the exams again, you might find out that some of these schools do, some don't, but this will help you to know where you stand or if you need to move on with schools.
If you are in the waiting list, call and see what the chances are. Keep in mind that the 2009/2010 generation is an overpopulated generation due to the baby boom in 2009. The uptake of private schools has grown for secondary placements after these lockdowns, so be as realistic as possible of the chances that your son might have in moving up the list. Bottom line, he might still be up for a chance if he is in a waiting list.
Going down the prep school route:
The advantage you will have is that there is room in most schools who are running Y7 and Y8, as other have mentioned, due to the exodus at 11+. Those that might get you in the schools you mentioned, most likely will have their own entrance exam that your child will have to take. This will also give you an opportunity to see if you have a chance to make it in any of those schools.
My only advise here is that you are upfront with the Head and talk about your aspirations for your child. They will be a good gauge depending on the school and on their exams, if you child actually has a chance to make it in or not. But they will also give you other options that you might not be aware of.
Please note that a lot of prep school children whose parents had the schools you mentioned in mind, have also being tutored (not all of them), but a good number have. The competition in London and the SW is criminal and throat cutting for selective schools and even the mild or no so selective ones!
A tutor could also be a good port of call, but they are hard to find in London, but never say never.
Please bear in mind that a prep school or a tutor does not warranties the placement, it opens up the possibility and gives your child an extra tool to have a better chance, but is not 100% proof. Some prep school children didn't get the school they wanted at all.
Your child:
Before going on this issue, you mentioned that there were particular circumstances that affected his performance. Plain speaking, parents divorcing, death or bad disease affecting an immediate family member or a bad accident are circumstances that would get your child an opportunity in caring pastoral schools such as Reeds in Surrey, worth checking them. These have to be extreme circumstances of course.
You know your child best and you will know what would suit him best. We have chosen, despite the advise of the Head, a non selective or how they call themselves a mildly selective school as although he has high CATs, he also performs extremely well in maths, apparently he is KCS candidate with your eyes closed, whatever that is! But he needs a nurturing and less demanding placement. We needed a school where he as going to have more an almost 1-2-1 rather than being one more of a lot of brilliant and clever children.
I hope this has helped!