My school-hunting days are over, since my youngest is now in Y9, so my info may be out of date. But Mossbourne certainly used to think it was the answer to everybody's prayers, and there are a number of other popular schools that give off that vibe - Alice Owens and Latymer always had that feel to me. But any school that is incredibly over-subscribed or suddenly becomes fashionable and sought-after can go down that route, and not for the better. Pro tip - when you get to the stage of looking at schools, phone them up at some random point and ask a mildly dozy question about open days or admissions procedures, and see what kind of response you get. There are a number of popular schools, state and private, where the admin staff emit a strong sense of, 'Oh god, not another stupid parent wasting my valuable time'. And there are other, equally over-subscribed, schools that fall over themselves to be kind and helpful to clueless prospective parents. Yes, obviously the people answering the phones are receptionists not teachers, but IME that gives you a small insight into the attitude of the school as a whole, and the kind of reception you can expect a few years down the line when your stroppy 14yo is being pointless and annoying and you want the school's co-operation in dealing with it.
The thing I like about HF is that they've serenely kept on doing what they do, apparently impervious to the various schools fads that have come and gone - they've still got the 1980s style polo shirt and sweatshirt uniform, they've resisted the pressure to adopt fancy ties and blazers, or various kinds of academisation or covert selection. And this is despite the fact that they must have come under significant competition from the huge changes in other parts of the local education scene, like the start-up of SMM, the various Hackney academies or Highbury Grove's stellar rise and ignominious fall etc. They've just kept doing what they do, being a successful local comprehensive for a very mixed intake. That would suggest to me that they have a strong sense of where they're going and aren't at risk of the kind of gimmicky fashion disasters that other schools have fallen victim to.
So I'd go and have a look, no harm starting in Y5 or earlier, and if you like what you see then you're probably onto a good thing. Go and look at other schools as well, even if you aren't seriously considering them, since the differences between them are quite revealing - sometimes you have to see something you don't like in order to realise what you do want, iyswim. If you're concerned about the academic level, then have a look at the top end of the results and see what they're doing for their high-achievers - if they have a reasonable number of girls at the top end coming out with a healthy string of As and A, then there's no reason why they can't do the same for your dd, plus your dd is likely to find a good cohort of like-minded souls to hang out with. The overall headline results like 5 A-C are less significant, since that mainly reflects the intake as a whole rather than giving you a steer on what they achieve for girls of your dd's profile.
I've said this on here before, with varying responses, but it may bear repeating: I've seen my own four dc and their various cohorts of primary school friends go through the full range of schools, from local sink schools to super-selective state and private. And without exception, regardless of the type of school selected, all the dc have come out with pretty much the grades that you would have predicted for them at the age of 9, based on their abilities and personalities. I know of dc who went to very rough comps that have gone the straight A* and Oxbridge route, and kids from super-selective schools who have come out with extremely mediocre grades (and a slightly battered sense of self-worth as well). So if you can find a local school where you think your dd will be happy, and that has a good track record of getting dc of her ability the grades you would hope she is capable of, then you can't really do fairer than that.