I think the independent sector in London is the most stressful of all.
There are a few super-selective grammars in our area (south-west London). Children are tutored for years in verbal /non- verbal reasoning and the highest scorers will get the places. Fair or not, everyone knows the deal and it's as simple as that.
The independent schools are equally, if not more competitive - not only the "top"ones like St Paul's or Latymer Upper, but also the supposedly "broader intake" ones. It is usual for children to sit 5 different exams at 11 plus, not only in reasoning, but also in Maths and English. Even an excellent performance in the exam is no guarantee of a place if you don't have the personality or confidence to then get through the interview stage. It is perfectly possible for a child to do 5 separate exams and not be offered a place anywhere. It often feels like there are no schools for an academically average child because if schools can "cherry pick" they will.
State schools vary hugely and it can be more expensive to pay the stamp duty to move into an area with a good school, than to just stay out and pay school fees!
Those applying to Catholic schools may find that places are offered according to the age of the child when he/she was baptised. This is even more ridiculous.
At DS' school, 1,300 sat a 4 hour exam for 120 places. From this, 400 were interviewed, at which point the child's interests, self-confidence and personality are assessed as to whether they are a good "fit" for the school. A child could have performed excellently in the exam, but still not be offered a place based on the interview or previous school report.
This is why people in London may get worked up about school selection policies!