I've just seen this; and am in the same situation (I don't think anything has changed in 10 years).
My son has done really well at school at being a "good person", and in Maths and Science and everything else BUT English. His comprehension is not that good and he's come out at lower than expected in his last mock English SATs test. They have more tests this week. I've read all the posts above. There are parents on our year 6 whatsapp group asking for recommendations for tutors etc to get their kids through SATs.
IMHO, I don't see the point. If my son has help now, and gets better SATs grades for English, then likely he'll be placed in a higher set in year 7 at big school. At which point (without the continued support of a tutor) might just find it too difficult to work and learn at that higher pace.
If he starts getting better then he can always get moved up a set (as I was frequently at school) but if a slower pace of learning for English is where he's at, then surely that's the right place for him?
His mum and half sister also have Asperger's, a symptom of which (strong in them both) is taking things very literally with a poor understanding of metaphor, sarcasm, subtelty etc. It does ring very true to my son I think; he tries but gets very upset that he just "can't do it". To be honest, the comprehension tests I've done with him, I didn't get a very good mark either, and I got As at GCSE English language and Lit. The passages they used (from which you had to answer questions) were extremely poorly worded. I will give examples if anyone wants to know - be interesting to see if I'm just being thick or whether they are actually not very well worded/thought out.