Yes, it is extremely important that you list the schools in your true order of preference.
The allocation of school places is coordinated across all the London boroughs and Surrey; on allocation day your son will be offered a place at the highest preference school that he is eligible to attend.
Only the Local Authority knows your order of preference. Each school will tell the local authority which of its applicants is eligible for a place, and in which order. So for the Grammar Schools, eligibility is determined by passing the test and rank order of scores. For community schools, eligibility is determined by distance from the school, having a sibling there and so on (each one will be different – do check).
So if you’d really like your son to attend a Grammar School, but you put a local non-selective school for which your son is eligible ahead of the Grammar on your Common Application Form, then you will be offered a place at the local school, even if your son has passed the grammar test. In this example, the non-selective school is the highest preference school that your son is eligible to attend.
Alternatively, if you have placed one or more Grammar Schools at the top of your list and he does not pass the test(s), this does not jeopardise his chance of getting a place at the local school that you have listed as a lower preference – because the local school then becomes the highest preference school that he is eligible to attend.
It is extremely important that at least one of the schools that you list on the Common Application Form is one that you are happy with and at which your son is highly likely to be eligible for a place. Otherwise the Local Authority will have no choice but to offer a place at any school where there happen to be vacancies.
So it is best not to fill your Common Application Form with Grammar Schools only. Have at least one local non-selective school on the list.