Funkychic I'll hopefully be able to tell you more tomorrow...I'm a bit shocked the mums you met haven't been able/willing to give you more of a lowdown given that their dds are in as it were. Though Xenia's point about the girls' own recollections or lack of them, given their age could, to be fair, have a bearing too.
I didn't tutor my dd, though I did have to do some (mainly oral) times tables with her beyond what she was covering at her last school, in order to cover the outline "syllabus" as provided on a sheet of paper by NLCS (you'll have seen the one I mean!).
I'll ask the mums whether anyone tutored for 4+, but I can't guarantee you I'll get a straight answer...certainly some of dds ex First School friends were at pre preps before their 4+, - so perhaps more of a fast pace/tutor like vibe there (?) and some at gentler nurseries. What I'm interested in for you is whether any of the First School girls don't make it through to the Junior School at age 7; will try to find out. Maybe Xenia knows ? You wouldn't want your dd to get in, only to find a highish number of year 2 girls being asked to go elsewhere rather than on to the Junior School.
I'd say please don't tutor your dd, even though I take on board your concerns about the August birthday issue. I note from my dds year 3 list of 2 classes, there are quite a few July and August birthdays, some of whom i know for sure were at the First School. In fact a parent at one of the Open Days last Autumn, prior to dds assessment, raised this very issue, and was told they take full account of it.
It's possible to tutor a child to get into these schools I'm sure, but I'm equally sure they wouldn't keep up if they weren't supposed to be there, iyswim. I haven't (yet) any tales of woe re the First School, but have heard from other parents about the occasional child who leaves the Junior School after, say, a term because she can't cope, or who struggles on for longer, only to be told around year 5 that she's unlikely to make it to the Senior School. Often these poor girls have been over tutored to get in, and a short time later it all falls apart.
But hey, enough of this ! Most people love the school, and it's an unparalleled experience for the right girl. My dd is ecstatically happy and thriving. Will post again tomorrow.