Someone will come along and post a link to Atom scores and schools shortly (I can never find it!), but what I would say is look very closely at the exam format for the schools you are interested in.
I live in an area where people tend to sit both the (full county) grammar and independent school exams. A lot of children who have mainly used Atom got a bit unstuck with the grammar test as it is paper based and has a separate multiple choice answer sheet which you put marks on. They knew the stuff but hadn’t actually practiced real world things.
Likewise those children who had practiced specifically for the grammar test found the ISEB 11+ harder, just in terms of adapting to the computer based format.
You then have schools where everything is written like a more traditional exam. You’ll get marks for your workings in maths and will have to write in complete sentences, they look at your spellings, grammar and punctuation etc. If there’s a creative writing piece then do they know how to structure a good piece of writing.
Some schools it’s fine to worker slower but more accurately (like the ISEB). Grammar tests, speed is a lot more important. You can afford to drop a mark here and there so long as you get through the volume.
Some tests you can skip questions and then go back to them. Other tests you can’t.
Exam technique and timing is often overlooked by parents tutoring at home and it’s so important.
To add that by the time the exams came round my DD was scoring about 121-125 on Atom and has been offered places at all of the schools we applied to. A mixture of selectives (although not super selective), grammar and regular independents.