I very much doubt that the school is taken into account in any area of the UK. It certainly isn't in our area. Age of child is, as you probably know, taken into account more often than not. (It isn't in our area).
Please don't be disheartened. Look at the practice papers on offer via this sight, for use at home. You can go through these with your child yourself and/or employ a tutor. It is a matter of personal preferance.
You should remember that the schools in your area which do help children prepare for the 11+ won't have time to devote wholly to it. They have the end of year 6 attainment tests and the general curriculum to contend with as well. Therefore, it is possible that your child, if working on 11+ practice at home, may be at an advantage. Certainly, there may be some parents who think that the school is doing the job and that they do not need to add to what their children are doing for the 11+ at school. You, on the other hand, can dedicate as much or as little time to the project as you, your child and the rest of your family and life will permit.