There's enough time, but I agree with mumblechum2 - he needs to be getting 90% or above in August (at least 3 weeks before date of tests). If you can't help him with the work, get him a tutor. You want him to get away from the bullying situation, right? And to give him more choice about what schools he can apply for. Think of the boost to his confidence it will give him when he does well. A good tutor will also help him to approach his work in a way that will help him when he's on his own in secondary school.
Don't buy into the myth that your child is not capable of tackling his homework in a different kind of school just because he got some tips from a tutor for one set of exams. He's going to a grammar school, not to Cambridge University's PhD programme. Pupils often fall behind in grammar school for two main reasons -1) other normal problems related to ssecondary school: becoming a teenager, developing more interests in new sports & hobbies, settling into a new school, social/family porblems, a school commute that is too far, etc etc, 2) the teaching and structure of the school being unfamiliar (maybe a big class compared to a smaller previous class).
Also, nothing to stop you getting a tutor for the odd problem subject when he is grammar school if he really falls behind in that and isn't able to get help in school. If you haven't enough funds, that's one thing, but don't assume he isn't capable till he's given it a go, and had a bit of guidance to help him give it his best shot. Just my two pennies' worth. Wishing him the best of luck!