I have children both at ASL and British private school. I believe that ASL is one of London's top schools - otherwise why would I send my children there. However, it is all relative to what you come from. The facilities and resources are great but not better than what we had back home. The math program is lagging compared to our US private school.
A math tutor in general maybe good for your child if his math program at school is lagging your expectations. The material tested on the ISEE are standard concepts. Buy a prep book. You will see what concepts your child should master such as: probability & data analysis, fraction, decimals, percents, some algebra, geometry, measurement (US units). If you do enough practice tests, you will see repeated concepts such as calculate area, perimeter, mean, median, solve for a variable, compare fractions, etc.
Children generally test high in either Verbal/Reading or Quant/Math.
Your son's math score on the practice test you took maybe due to the "American wording" of problems. Believe me, it is a struggle to understand when you are use to different wording (UK vs US).
ASL has an Admissions open house. Check the website. I don't believe school events are open at all to the public because of security measures. Search for ASL youtube videos online which will give you an idea of what the school is like.
Spots always open up in each grade but they are not many. I would guess the new students in each grade are about 15-20%. I don't recall the statistics exactly for this year but each middle school class had about 20-25 new kids (average). I have no idea how many apply to each grade but it must be a lot given the waitlists even with a 29-30K yearly tuition. About 2/3 of the school population has been at ASL for over 3 years. Some of my child's best friends have been at ASL since kindergarten (reception) and will probably be "lifers". Turnover is not as great as many think. Maybe that will change over the next few years given Brexit. This year about 40% of the new students came from the US and 25% from international schools. More than 1/3 of new students already lived in London. Siblings do get priority for open spots over a new family applicant. This reduces the spots open to new families.
You do see a lot more London families apply to ASL for Middle and High School. You will find ASL students who have been educated in the UK system up until Middle / High School. Typically, they make the switch because they want to attend US universities.
One thing I can assure you is that ASL is very welcoming. Students and staff know how difficult an international move can be or starting a new school. There is always someone who remembers what it is like to be the new kid and wants to help out. Administration has an open door policy where you can reach out to them if you have any issues.