London 11+ private schools is a horrible process - so many high achieving and tutored kids all applying to the same schools.
I am not convinced by “trust the process” and that a rejection means it was the wrong school for your child. I think so much of it is down to luck.
These schools are having to decide between hundreds of kids who are all at a similar level, so their choices based on a few marks’ difference and maybe some minor elements in their school report or extra curriculars.
Ok there will be some kids right at the top who will clearly get through and some right at the bottom who clearly won’t (and their parents probably knew it was a long shot) but in the middle there’s hundreds of kids who might or might not get an offer depending on how they did on that one day and with that specific paper.
This can depend on whether they slept well or badly, felt a bit ill, had a good idea for the creative writing or not, had seen that kind of tricky 5 point maths question before or not.
I have told my daughters this and I hope this means that if they get a rejection they will know it isn’t them being “not good enough” but just that on that day, that paper suited someone else a little better.
It’s a horrible process and doesn’t really select the “right” kids for the “right” school IMHO.
However, to balance this out - I don’t believe there is all that much difference between these schools in the end. Your child’s experience at school is going to depend way more on things like who is in her class and does she like her teachers (and you can’t predict these things), rather than on whether she went to Latymer or Francis Holland.