Applying for private schools in NW London is a crazy thing to have to do. For example, SHHS will only assess 250 girls. They give out the forms on a certain day, about 18 months before the assessment, and have a queue of parents outside the door for hours before they open on that day to get a form. A picture of the queue is usually in the local paper.
You need to apply for a spread of schools regarding competitiveness. SHHS, NLCS, Channing, Habs and St. Christophers all have at least 10 applicants per place so you need some backups. Northbridge House is less competitive. Go and look at St. Margaret's in Kidderpore Gardens - it's a really nice, very small school that is again a lot less competitive and is looking at the individual girl, not just how docile and well trained they are. I really liked the head, Mr. Webster, and it has an unusually high percentage of male teachers which is unusual for an all girls school. I believe that the schools in Mill Hill are also less competitive, though I don't know much about them.
A backup is to have a place at a pre-prep lined up, such as Golders Hill, Hampstead Hill, The Avenue, or Annemount. These aren't selective -it's just waiting list - and they go through to 7 and will then prepare your daughter for the 7+. SHHS, NLCS and Habs all have large entries at 7. Norfolk House is non selective and goes to 11 but it's in Muswell Hill, so probably a bit far for you.
If you want a lot more info, search for the MN poster mumteacher and her threads 3+,4+,5+ support - but have a stiff drink to hand if this is your first indoctrination into the bonkers world that is NW London private schools.
Best of luck to you, you're going to need it.