Goldie, I've come late to this debate but
She's going in to year 7:
It is very likely that should she be unhappy or as Colleger suggests, insufficiently, stretched, that you could move her pre GCSE in years 8 or 9 into the private sector - private girls' prep schools don't quite so often go up to year 8, but quite a few of them do, so she would not be so unusual. Perhaps not the one closest to you, but you should be able to find a really good one, if she is so able. And she'd cope socially, I feel sure, from what you say.
But to move any child into a super selective grammar at year 8 or 9 is usually not so easy. The switch only goes one way, normally.
Don't also forget to do your actuarial and economic calculations on how inflation will affect private sector fees.
IMHO, take the grammar, sigh with relief you don't need to pay those fees for at least a year, be prepared to move pre GCSE or then at A level should you want to. And see what it takes to stretch her.
And I pay for DS to go private!