Do you mean 11+ exams for state grammar schools or 11+ screening exams for a less selective independent school? Does his current school go on to 13 or 18? In which case there is less incentive for the school to push at this stage. I agree though he might struggle at grammar school (if that is your plan) unless there is a clear explanation.
Has he been tested for any SEN? Does he seem to you to be verbally more able than his scores reflect? Remember 100 is 'average' so if he seems like an average boy, maybe he is and maybe a highly selective school won't suit him.
If he seems more articulate than the scores suggest then perhaps there is some reason. Does he have any other symptoms. How is he when he reads to you? How are his spellings? Writing? What sort of errors does he make in maths - is it that he doesn't understand it or he understands the theory but it falls apart when he gets a written question?
My dd has just been diagnosed with something that affects her work and yes it would affect her CAT score, but is also treatable (to an extent) and so although her scores might be low, with some acceleration she might manage in a selective environment with appropriate glasses.
If you don't suspect any specific issues and it is just 'who he is' then maybe a less selective school and maybe he is a late developer. Some children suit secondary school more than primary and maybe he will come into his own with a greater emphasis on humanities and sciences.
Unfortunately in all schools as parents you have to do the pushing and find out for your dc what the issues are. We were told for many years that 'she is meeting expectations and is where she needs to be' because basically their view is average in average out. Unless a child starts slipping back in targets - achieving less than expected progress or is substantially behind it doesn't trigger any intervention. We have pushed really hard and have been lucky to have a great teacher this year who has seen her potential and has seen that dd on paper is quite different to dd in person.
If you describe here some of his issues you might get some answers or describe his work on primary board. People will probably focus on the fact that you are trying to get him into a selective school and on paper his scores won't justify that. If there are specific issues though someone on here (teacher/parent) will probably have already seen them and have got the t-shirt!!