I'm going to have to be pretty immodest here but he found it absolutely fine. He had some amazing teachers and, especially in the earlier years when they are not teaching to a specific GCSE, he had his brain opened to all sorts of interesting ideas. He was not made to be overconfident either.
He did come top in their 11+ scholarship exam though so it's not a good test and the interview was fun if they still do that.
It's a very competitive place. He's not into sport at all but that didn't seem to matter too much. My own brother went to Bancroft's in the mid 1970s and it was much stricter and single sex.
DS also got into Ilford County High for Boys but as he got a half scholarship to Bancrofts we decided that was school of choice (and a better journey).
I wasn't sure that he would get a scholarship because, like your DD, he was top of everything at his state primary but really I didn't know if he'd still be as bright at Bancroft's. There I would say he was always in the top 3, except for music.
His older brother did get in too but didn't get a scholarship so we couldn't afford to send him, although he went at 16 for A levels only. Both DSs found it occasionally intimidating that "everyone" went skiing in the holidays (not us) and quite a few kids had brand new cars for 17th birthday presents.
Personally, I loved the buildings but according to my sons you get used to them very quickly.
I hope that helps. You can PM me if you want.